They don't have shows in every STATE but I believe they have shows in every region (as they define region). A mini only has to have 2 square inches of qualifying white (and no app characteristics) for registration. It helps some if they are AMHA or AMHR registered as those are approved "outcross" registries, but they don't have to be. At some shows you can even bring your photographs and get your horse registered right on the spot and then show. In New England, that is very common. They do have to be registered in order to show at approved Pinto Shows and earn National Points. In our area the shows offer halter (1 class, all sexes and sizes), color, trail in hand, hunter, jumper, obstacle driving, pleasure driving, disciplined rail driving, ideal pinto driving, and a Day End High Point that includes all those classes. Those classes will be different in different areas and change over time. The Association also offers classes in miniature gymkhana driving, roadster, fine harness, and costume. Lots of variety and fun.
P.S. Photo in avatar was taken at a recent Pinto Show.