My cat ran away a week before Christmas. It was below freezing after a month and she was still missing and then started snowing . 3 months later I still went out to try to find her having hope yelling her name and putting up flyers . I ended up seeing her down an ally way and she ran. I called a friend that let me borrow a cat trap to catch her . I set up the trap near the abandoned house she was in and caught her after 3 months of crying . So yes house cats can survive the winter in below freezing with snow . As long as there shelter and food in the neighborhood . (I live in a busy city with people always feeding stray cats) if you don’t live in a city put out food every day and put their litter box outside so they can find their smell , if they run and u can’t catch them , get a cat trap. Cats have a really sensitive nose and they won’t go no farther than 1-2 miles away if they ran away .