A "hat collection" refers to a group or set of hats that someone has gathered or owns. It could mean they have multiple hats for different occasions or simply enjoy collecting and wearing hats. Full definition
But if your signature is a hat, you can build your wardrobe around your current hat collection. (40plusstyle.com)
Sure, I'd have the odd baseball cap or bucket hat in my collection over the years and in my youth, but my adult hat collection was almost non-existent in college. (hellorigby.com)
Neither of us have a crazy hat collection, but it's slowly growing! (funinthecloset.com)