Tyres are the most important part of a car, since they're the bit that actually interfaces between the mechanism and the medium.
Normal tyres aren't as grippy in the cold since they harden up. This might be fine 99% of the time since you'll be more careful in these temperatures anyways. The last 1% of the time, the grip you get could help avoid an accident.
It's cheap enough as a form of insurance; $100/corner if you don't have a monster of a car. And they last for several years.