Risk of fire inside the vehicle and carbon monoxide poisoning jump to mind.

I have been stuck in my car in winter storms twice: once for 12 hours and once for 6. Both times it was on a major highway near Washington D.C. You don't need to be in the boonies.

The better solution to starting a fire inside the car is to carry sleeping bags, wool blankets or heavy coats, hats etc. with you. Inside the car, you are out of the wind and the wet: all you need to cope with is the low temperature. And all you need to do that is to cover up with insulating cloths/blankets etc.

I always have some in the car in the winter.

That's certainly the best approach. But these were both situations where someone else's truck or plane got stuck when people were on an adventure holiday.
Personally I'd be; 'This sleeping bag isn't leaving my side and I'm not getting on that plane till I see a beacon and a survival kit!".
qjs

My car contains an entire duffel bag full of spare clothes, outerwear, and a nearly new pair of boots. It takes up a lot of trunk space but I think it's worth it. My oldest daughter loves it too; I keep a sweater in there that she likes to snuggle with when sleeping during a long drive.

Try vacuum storage bags to reduce soft goods storage volume dramatically, while also giving them decent dust- and water-proofing.