I live in Siberia.
First, roads that are cleaned in winter have significant traffic. Less important ground tracks get covered by snow and impossible to use in the first weeks of winter. So if you're driving down a highway in winter, at least minimal traffic must be there, even in remote areas.
The more remote you are, the more likely people will help you if they see a stopped car.
Problems start if you suffer break down at night, when traffic is almost absent in frosts below -25°C..-30°C. In some colder and drier places like in Yakutia, there's not much snow, so roads are cleaned rarely and seem maintained and used, but traffic is almost nonexistent in the coldest days.
So, the simple precaution is to go in 2 or 3 cars between cities, to help each other.
On Burning Tires
I heard anecdotes of people getting stuck in such conditions, but on major highways, and being saved. Some of the stories mention them having burned almost entire car: gasoline, seats, tires, etc. And usually they did this within a couple of hours.
So burning any stuff outdoors, as Sergey Gulbin suggests above, is barely useful. It won't keep you warm long enough. Everything gets burned soon, and still there's no by-passer, and you're doomed. Burning wood is problematic too: live trees burn poorly, dry trees and logs on the ground were wet in autumn and now have a lot of frozen water in them. Tourists do use them, but with help of other fuel, and definitely not in an emergency.
Secondly, if you try keeping small fire outdoors over long time, in such frost, you surely get nose and toes frostbitten.
Not to mention poisonous smoke, and that extracting gasoline from the tank and burning it is a stupidly dangerous act.
edit: Extra note: car body is made of metal which conducts heat easily, and in extreme cold is a bad shelter.
What to do
Prevention measure #2 have a truck drivers radio if possible. Then getting help will be very easy.
Above things mentioned, I'll point out the key measure: shelter. Winter tourists go hiking for a week in -20°C and come home unharmed thanks to tents, sleeping bags and tourist gas cylinders to heat up food, melt snow, and boil water. Since gas is finite, they still have to gather some wood, but for one night or emergency, one cylinder is more than enough.
So take a few things to make a shelter:
- either a minimalist tent or 2) a big enough piece of hard textile and ropes. 3) at least a lighter, or small gas cylinder and burner. 4) maybe a winter sleeping bag, if you have space for it.
If snow is deep, digging a shelter is quite easy. Make a pit and an entrance downwind, then cover the pit with the textile/tent, leaving small hole for ventilation, and cover from above for more heat insulation. If snow is shallow, use terrain features as protection from the wind, and probably put some snow above the tent to serve as extra insulation. (Snow depth depends a lot on region, some have just centimeters, while others have 1 meter by the middle of the winter, when dangerous frost may happen.)
Then make it noticeable to the bypassers that you need help.
Regarding probably fixing the car, as Knuckleballerr suggests, I'd say it's safer to make a shelter first, then have a safe place to retreat if you can't fix it.
