I live in Siberia.

First, **clean roads in winter are used by traffic**. Minor ground tracks get covered by snow and impossible to use in the very first week of winter. If in winter, you're driving down a highway, it means it's been cleaned by tractors, and this only happens in important roads. So you will happen to be on a road with at least minimal traffic even in very remote areas.

Second, we usually go in two or three cars between cities in such weather.

The danger is that in days of frost, below -25°C..-30°C, traffic decreases from few hundred or thousand cars per day to a few cars per day, and probably none at night.

**On Burning Tires**

I heard stories 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 in couple of hours, and still there's no by-passer, and you're doomed. Burning wood is problematic: 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, so it takes a lot of effort and other fuel (like liquified gas) to set them on fire.

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.

**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 have things to make shelter:

1) 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. 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.