Balla Hat

It shows up in the Clothier list only after the Frost Legion has been beaten, which means you need a Snow Globe and a fight first. On current versions he only sells it while the sun is up, so a late-night shopping run will come back empty. Older console and handheld builds handed it over free at any hour.

It is the same hat the Snow Balla enemies wear during that event, and the shape is the bowler that films have been putting on 1920s gangsters for a century. Despite the snowy origin it does not read as winter gear at all, so it fits a suit-and-tie vanity set better than anything you would wear in the tundra.