Bike paths don't have to be dry though, you can sweep them and it's fine. If you use studded tires, you can ride a bike in places where you can't even walk. Source is I used to do this when I lived in the middle of nowhere in Sweden. I agree with you that infrastructure is key though. The temperature doesn't really matter, if you're good to go on a walk, you're also good to go for a ride.
I see bikes in the summer here. I dont see almost anybody biking in the winter here. Like 100:1. The winters here are not mild (like in vancouver). This is basically artic-like weather. People also tend not to walk. The very poor take the bus. Most drive.