A Ten-Gallon Hat is a brown cowboy hat for your dogs to wear. It is tan coloured with a brown belt around it and a buckle. In Nintendogs + Cats, it was renamed "Safari Hat" and it also comes in a white version. It can be unlocked by having 5,400 Owner Points and can be bought at the Mountains BARC shop for $50.
DS: "Put this on to experience the rootin', tootin' atmosphere of the old west."
3DS (Brown): "Embark on a wild safari with this practical-yet-sauve hat."
3DS (White): "Prowl the untamed savanna in style with this rugged-chic hat."