With the onset of winter it can sometimes be necessary to cover your ears to stay warm. As I was recently reminded by a reader, that's hard to do with a homburg or fedora. Which makes it time to reach into the back of your closet for your ambassador hat (like the one in the photo) with the pull-down ear flaps.
The best ambassadors that I know of are made in Canada of water-resistant beaver fur ($385), though they also come in mink. You'll find them at the A Suitable Wardrobe store as well as local hatters.
Living as I do in Northern California my ambassador has had about a decade of rest since its last trip to Switzerland (I try not to travel to cold weather cities between January and March). But I still have a vivid memory of sweat pouring off my head after I spent a few minutes inside a shop without removing it. They're very warm, and that's usually a good thing.