American games will handle the cold a little better than the hard feathered asil, you can dub the brood roosters you wish to keep through the winter, if you don't the frost will, either way it is not much of an issue. The hens usually have small, tight combs.
If you are planning on letting nature take it's course and using gamefowl to self regulate on the excess males, it is not going to be real pretty. The ones, or more like one, that you have left probably won't be much to look at. They put out eyes, scalp each other, break wings and all sorts of things. The survivors might in fact be the ones that aren't very game at all and run and hide whenever they hear trouble. Likewise you could end up with survivors that weren't able to breed, or even no surviving roosters at all. They don't tend to notice predators real well when they are facing off, and it would be possible to have one kill another and die later from injuries. Another problem, if you are using the asil, it won't just be the roosters self regulating, the hens will do a good number on each other as well. If they have small chicks, they might get caught in the crossfire. I don't mean to rain on your parade, just throwing out some possible outcomes. I suppose if you add it in and then mix enough other stuff to breed it back out, it might work, but to retain the traits that you want it will be a lifelong project.