I have heard that in cold conditions, you'd freeze faster wearing wet clothes than not wearing any. I cannot find any proof that this is true. Is it?
This depends on the actual type of clothing and mostly on the wind speed.
The wind evaporates moisture from the body. Since evaporation is a cooling process and absorbs latent heat away from the body, the person feels colder. Skin always has moisture on it. Just like a tree transpires, the human body is constantly having water evaporated from it. Wind intensifies this process. A hot day with a breeze will feel more comfortable than a hot day with calm wind. Wind and evaporative cooling are closely linked. The higher the wind, the greater the amount of evaporative cooling, especially if air is dry.
If you have an efficient outer wind impermeable shell, your inner fleece layers will warm you even when they are wet. Therefore it's better to wear something, even if you sweat due to activity. Still you won't feel that comfortable with wet clothes.
It depends a bit on the circumstances.
If you have just fallen in freezing water than stripping off will probably get you warm faster as wet clothing will usually conduct heat away from your body faster than just cold air next to your skin.
However, in cold conditions, being naked is not good for even short term survival, so once you have your core temperature up again you need to get some insulation on or some other external source of warmth (e.g., a fire).
Equally important is that wearing wet clothes is likely to be the fastest way to get them dry. Wool base layers are particularly good in this context as they retain a significant amount of insulation when wet.
In some cases, a good compromise is to take off your mid layers and wear your base layers (which dry very quickly) and your shell layers (which shouldn't get wet as such anyway) temporarily discarding your mid layers which tend to be what soaks up water. This will provide you with some immediate protection.
Having said that, you should dry your mid layers as quickly as possible. Fleece and (even more so) fur-pile dry very quickly and provide useful insulation even when damp, so wring them out and hang them up to dry in the wind while you run around, build a fire, or make a hot drink, and then put them back on again.
Also, if you are getting soaked from rain to the point that you are in trouble, you may be doing something wrong, and in borderline cold/wet conditions it is always wise to keep your sleeping bag and even some emergency insulating clothes in a waterproof bag so if the worst comes to the worst, you can just climb into your sleeping bag to warm up.
Furthermore, a well chosen clothing system should not fail completely even when really wet. You may be a bit uncomfortable, but you shouldn't actually be in any immediate danger. For example, for survival, you shouldn't rely on your outer shell to keep you completely dry.
It does depend on the circumstances and the other two answers cover it pretty well. A personal experience to back those answers up: I found myself sleeping in a precarious place after a rain storm which drenched just about all my gear - I was unprepared and did not have a dry bag of spare clothes. Overnight I hung up clothes to dry as well as they could, but weather and location didn't help much. In the morning, with my gear still wet, I rung out my pants and socks as much as I could before putting them on, then put on my outer shell which was still wet but provided wind protection. Before I did all this, I jumped around a bit to get my blood flowing - my sleeping bag was mostly dry but I was soaked and cold getting into it, so I had little warmth to start with and some exercise helped generate some. Expending energy was not a major concern because I just had a few miles to hike back to civilization.
On the hike back I was extremely uncomfortable with the cold, wet outer shell against my cold skin. Dry clothing in between would have been immensely useful. Still, I noticed that when I took off the outer shell, exposure to the cold wind was far more bone chilling. I kept the shell on and walked back. In this case, protection from the cold wind was precious, even if it meant wet clothing which would suck some heat off of me. If wind was not an issue, the wetness of clothing sucking heat off of me might be worse than exposed skin I could keep warm with exercise. Even then, I'd be quicker to remove a wet cotton shirt than a wet fleece, and that depends on how wet the clothes are and how insulating the clothing is when wet.
It is critical to have a dry bag for a spare clothes that never get wet unless as the literally last resort - better to wander about naked and have dry clothes to maintain your body heat in overnight if possible.
In cold weather, your first priority should be to keep your clothes dry.
- Wear waterproofs.
- Dress lightly enough that you don't sweat - it's better to start your day slightly cold than to start it hot and end up damp and frozen.
If you cannot keep your clothes dry:
- Wet wool or fleece is much better than nothing.
- Wet silk, leather, and most synthetic fabrics will also keep you warm.
- Wet cotton is worse than nothing.
- Wet down is worthless.
Cloth traps air in its fibers. These tiny air pockets keep your body heat trapped against your skin. A good insulator, like down, traps more air than a poor insulator, like cotton. This is why down coats are puffy and weigh less than a wool coat or cotton hoodie.
When cloth gets wet, these air pockets fill with water, which conducts heat about ten times faster than water. Warm-when-wet materials, like wool, have fibers (or coatings) that repel water. This keeps some of their air pockets open. Dry wool is warmer and comfier than wet wool, but both are much warmer than nothing. Down, on the other hand, is a good insulator when dry, but when wet, is virtually worthless.
Cotton, in contrast, absorbs water. Its fibers stick together when they get wet. This closes the air pockets, making cotton useless for insulation. Worse, soaked cotton holds a large volume of water against your skin. Cold water absorbs heat faster than similarly cold air, so you get cold faster in wet cotton clothing than you would naked in cold air. Wet cotton is worse than nothing. In bad weather, cotton kills.