In the winter, I have a hat (actually a cap) in my coat pocket. And gloves too. I wear them if I need them, otherwise they just stay in the pockets. I figure, if I don't need a coat, then I don't need a hat or gloves either, so it's safe to leave all the items together in one package. Most of my coats have hoods as well, because especially if it's windy, I want both a hat and a hood.