I just picked up two foster kittens (about 6 weeks old) whose mom get hit by a car. Last week we picked up two kittens whose mom was dragged off by a fox (we have kittens for anyone in upstate NY that would like to adopt!). Because of what I see week in and week off, I am never an advocate of a cat being an outdoor cat (fleas, ear mites, tape worms, round worms are abundant with outdoor cats, as well as cat fights which mean tears and sores, as well as danger of getting hit by a car, or dogs), and since most of our cats are domesticated, it is not cruel or unusual punishment to keep them indoors. Generally indoor cats live longer, eat better, and have less diseases. On the other hand, if the only choice is to put it down, or acclimate it to be outdoors, out doors would be the better cchoice. In the northeast, in the winter, frostbite is a very real possibility. If you have a garage, a cat door would be great, and a place for the cat to get out of the bitter cold. They easily get frostbite on their ears and pads and private parts. That really hurts. A bed with blankets built up like an igloo that they can get into would be the next best thing.
Please be sure to check with your vet, to rule out UTI's or kidney infections. He may suggest meds for the cats.