A very popular question at the barn over this harsh winter - aren't they cold? In fact, clueless animal rights activists often campaign for horses to be kept in heated barns. The general public is often mystified that barn windows are open in the middle of the winter.
So, just how much do horses feel the cold? The answer is - less than we do, and not just because they have fur coats on.
Horses are cold climate animals. To a human, ideal room temperature is about 70F. To a horse, ideal room temperature would be about 50F. (That might be an interesting trait to give your aliens).
In most climates, thus, horses can manage in unheated barns, although we often put coats on them if it's very cold. Heating the barn, on the other hand, would be prohibitively expensive and closing the windows can cause respiratory complaints.
So, the simple answer is: Yes, horses feel the cold. No, they don't feel it as much as us hairless tropical apes.
(And these guys feel it even less - horses are the only livestock Icelandic farmers can leave on pasture all winter, as long as they get enough hay!)