Many adventurers have a stove on them, though not necessarily for the purpose you describe.
From "Obtaining Water from Snow and Ice" by Dryad (who offer bushcraft and wilderness courses:
Most mountaineers, and explorers travelling in cold environments,
carry modern stoves which use liquid fuels such as Unleaded Petrol,
Propane Gas, or Coleman fuel in order to melt Snow.
So you're in an arctic tundra or on top of a mountain, and you are in a tent with a stove on hand. Is using the stove to heat the tent a good idea? That depends...
Some tents are designed to be used with heaters. But,
The tent is not going to be nearly as good at holding in heat as your sleeping bag. And if you brought the appropriate bag, you should not need a heater.
Using the stove uses up your fuel. So either you are dooming yourself to not have enough fuel to melt the water you need, or you are bringing extra fuel - a lot extra, way more than it takes to melt some snow. Extra fuel is extra weight. Weight is usually kept to a minimum.
One of the specific stoves I link below says it uses 2 liters of fuel for 8 hours of use. I'm not sure how that compares to others, but for that particular stove heating would cost you 2kg (~4 pounds) per night heated. That is nearly 30 pounds per week, not including the stove's weight.
Warning: There are potential dangers with heating your tent, even if you use stoves and tents that were designed to be used together. You need to guarantee that you do not catch your tent on fire, and also that you do vent the gases well enough that you do not poison yourself. Even if you account for that, you need to be vigilant, as a blockage in your vent (eg: snow) could kill you. (credit @Gabriel C. for safety suggestion)
I think the only three situations where heating the tent make sense (and only 2 of them are a necessity) are:
if you can, and doing so would be easier and make you more comfortable. This is more a want, a luxury, than a need.
if you are in a place which is so ridiculously, brutally, insanely cold that it is difficult to get warm enough without heating. I'm not even sure if this would be a thing, but I'm raising it as a possibility. The people who have the experience to confirm or deny this would be very few and far between.
if you are improperly prepared. Essentially, you are in an urgent, or even emergency, situation.
It makes sense when you are treating yourself to luxuries.
Maybe you were willing to haul the extra fuel. Maybe you have a large party or hired porters. Maybe you brought solar panels for your devices or a passive solar heater (both of these things some people do bring on the type of hike you described).
Whatever the reason is that you are able, assuming you are able, now you don't want to cover your head at night, you want to get out of your bag in the morning to the luxury of warm air, and you want a place to retreat to in order to relax in a warm place when it is cold outside.
Remember, when people ask "What do I need or not need to bring on such and such a trip?" we keep telling them "Whatever you are comfortable leaving behind, do without, and bring the rest if you are willing to pack the weight." Well, some people refuse to car camp or even to RV camp if they cannot bring their hair drier, so I imagine there are people who would desire the luxury of a warm tent, and for them heating the tent makes sense.
If you say otherwise, I will tell you that having a tent at all is not necessary. ;)
In case you want this luxury, here are some random links to items made just for this which I found with a quick Google search:
A 29 pound oil stove. Fuel use is listed as 8 hours per 2 liters. If your group wants to carry the extra 40+ pounds, enjoy.
This winter tent on Amazon even comes with a chimney and a stove! More than 70 pounds though, not including fuel.
An all-weather tent with option for additional heater which is sold separately.
Because it's a beyond-frigid -135 degrees out!
Record low temperatures on Earth in the coldest places have gotten to approximately -135F (-95C)! I assume very few people go to the spots where this has happened, but there are some very brave adventurers out there who might want to experience the coldest our planet has to offer.
So you say, "But I could build a snow cave, and I could do it the correct way so that it would be very much warmer inside!" Perhaps. And the common claim is that no matter how bad it gets outside, if you've done your snow cave correctly you can enjoy a balmy 32F (0C) inside. But would that still hold true if it's a freaking -135 degrees out??? I don't know, but I would not bet my life on it. This might deserve another question.
Let's say that the snow cave can come up to freezing temperature though. Now what? You've made the cave when it's perhaps only -50 or -100 out. Will your body heat raise the temperature fast enough for you? Maybe. If not, you might say "I'll just use something to help with the warming a little bit, maybe crack open a hand warmer to help raise the temp until it gets there." But now we're back to warming the "tent". "Oh right, so I'll just keep it in my pocket so it warms me." Fine, you're not technically warming it, you're warming yourself, but that's a fine line. I could also say that the mere prospect of making a snow cave to raise the temperature is itself a case of warming your tent.
But what if you get there and find that the material is not conducive to creating a snow cave? Or, someone might complain saying "I asked about a tent, not a cave." (though I could say "Just put your tent inside the cave.")...
So let's leave the cave idea behind for a moment and talk again about just a normal tent on its own. So you want to try to survive, comfortably, one of Earth's record cold nights in a tent. Sometimes people double-up on bags. So let's say you get the extreme coldest rated bag available on the market, two of them actually so you can stack them, and a good bivy bag to go over the dual sleeping bags. And dress yourself very warmly, as warm as is reasonable for sleeping. Now you're in Antarctica during its winter, where it is literally night time all day long for days straight. Can your warm setup keep you warm enough through that night, where it gets down below -100F or -90C at least once?
In the super frigid arctic scenario so far, maybe you could be comfortable with the ridiculous setup in the previous paragraph. I'm not sold on the idea that you could though. At this extreme, I don't think conventional estimations would be very accurate. But even if you could be comfortable inside your sleeping bag, it might be easier at this point to warm your tent a little. At that huge a temp differential, a little bit of heating will go a long way. Just remember to keep your heater itself warm enough that you can start it. Still, at this point it might be easier to do a little bit of heating anyway than to just keep piling on more layers. Also, eventually you will probably want to come out of those sleeping bags and move around your tent during this Antarctic winter.
I have found supposed evidence of sleeping bags that are rated down to the record temperature, but I found them on forums where people were expressing skepticism about them. I'm not sold on that.
After a quick search for coldest sleeping bag, I found some that seem more trustable rated at -40F and -60F. Here is one, and another. They are the body form-fitting type, so I'm not sure how well they would stack. But if you could fit one into another thing that was -40F or -60F, even if I was wearing a good coat and multiple other good layers under that, and had a bivy over the dual bags, I still would not want to trust my life to that at -135F if it was my first time trying to endure that. I would bring body warmers to use inside the bag for a short stay, but for a longer stay where they won't last long enough, I think I would want something to warm the tent. However, that then raises other considerations, such as what do you warm the tent with since many fuels might freeze at that temp? Is it safe to bring a tank of propane on such a trip? The jury is out on this one, but I still believe it fits your criteria.
And I just realized another point when reading about obstacles that cold weather sleeping bag makers need to consider: the mere act of breathing in the very cold air from outside your bag. You cannot just keep rebreathing the same air again and again; it needs to circulate. At -50 maybe you can get away with minimal air heating by clever design that exchanges heat during air circulation, but at -135 even a lot of heat-exchanging with the warm air that's leaving the bag will still leave the air very cold as you breathe it in. Heating the tent will greatly help here and might be your best choice.
So, for someone wanting to set the world record for camping out in the coldest weather, every little bit helps and heating the tent would make objective sense.
Emergency! You're not fully prepared!
For whatever reason, you are not fully prepared. You are using everything you've got, and it's not warm enough. Maybe a freak ice storm, or you didn't plan ahead; whatever, you're out and you're cold.
In this situation, you do whatever you can to stay warm. I recently had a situation like this. I had two tarps with me, and no tent, so it was slightly different. I had one tarp on the ground, a small fire next to it, and the other tarp over top with one edge going over top of the fire. That is, I had an indoor fire in order to provide enough warmth. You could modify this for a tent though, especially in an emergency situation where you're willing to cut holes in your tent to accommodate a fire in the floor and an exhaust hole in the roof.
In fact, I can tell you that if I felt my life depended on it and I was using a tent, I definitely would rip a hole in the bottom of the tent to put it around a fire. It would be similar to the experience that I did have, mentioned above, except in a tent. I would be warming my tent based on objective reasoning.
If you are concerned about the safety hazard of an indoor fire, as you should be, or if you don't want to risk ruining your tent, you can keep the fire outside and use other things to warm the inside. Possibly other dangerous heating tools (ex: camping propane stove, gel burner, etc.) inside, or better yet just heat other objects, such as rocks, and bring them in (carefully! don't ruin your bag or tent).
Or use something to redirect heat from an outdoor fire into your tent: some kind of reflector, or a tarp to redirect warm air flow, or whatever you have. All of these methods are either too dangerous or unwieldy to use for warming your sleeping bag, so it needs to be the tent itself that is warmed.
If you have hand/foot/body warmers, like the chemical ones for example, then you should just use them in your bags at this point so you don't have to heat the whole tent.
Caveat on the emergency
If you are in this emergency situation, it might be easier, safer, and keep you warmer if you just go outside your tent and huddle close to your heat source. You can adjust your body's distance from the fire to keep yourself warmer than you would be inside the slightly warmed tent, so at that point abandoning the tent might be wiser than heating the tent.
Similarly, I have spent time curled up around tiny fires for warmth. Also, I keep one of those little emergency ponchos in my emergency gear, and I have used them to trap the heat from a fire: I started a tiny fire, put the poncho on, kneeled down by the fire and positioned the poncho so that it covered the fire and trapped warmth inside the poncho with my body and made me a lot warmer. In fact, the poncho example is specifically a case where I abandoned the cold tarp-tent to get warmer, and once my wife realized how much better I was doing she came out to join me too, so it is right up your alley as a counter-example.
However, when it gets cold enough, you can actually be hot on the side of you facing a fire and cold on the other side of you. In this situation, you could be better off with the tent ripped open at the bottom and put around the fire.
Basically, when heating a tent artificially makes objective sense literally comes down to "Because I want to" (ie: point #1), and "Because I need to" (ie: point #3 and maybe #2).
If you want to, you are willing to sacrifice something else for the luxury; that's what gear choice all comes down to, balancing by sacrificing in one area to gain in another.
If you need to, you don't have much choice. It's way freaking super cold, or for whatever other reason your gear is not sufficient.