I slept in temperatures in the teens recently, and was impressed with how well a sleeping bag and couple blankets (fleese and fluffy) work. I was so toasty warm I didn't mind crawling out in the morning that much.
Car batteries aren't made to be deep cycled, and their ability to tolerate it will vary greatly depending on the model and how old it is. A 50W blanket that's on for 8 hrs will consume 400W-hr of energy. That's getting pretty close to the sensible limit of a 100ah deep cycle lead-acid battery (which is ~600W-hr), so I think a starter battery subjected to that would die pretty fast.