A couple years ago, we had a passel of feral cats in the neighborhood. We used to feed and shelter 'em in our garage. We put a flap deal in the entry door so they could come and go. That winter was very cold and sometimes snowy. The ones that did not survive; eventually they were all killed off, were done for by cars, coyotes and other predators. They seem to handle the cold. On the other hand, your cat, if it's a house cat, may not have a winter coat like outside ferals do. It's gonna be sub zero here in Michigan tonight Bridgy. Put a box out with an old blanket the cat can huddle in. If you put out food, you may attract unwelcome guests.