* Wild Horses: While you can't catch and show a wild horse directly, you can show horses descended from wild horses, like mustangs.
* Miniature Horses: These are considered a separate breed and have their own show classes.
* Draft Horses: While some draft breeds are shown in harness classes, they aren't as common in traditional riding and jumping events.
* Horses with certain disabilities: Horses with severe disabilities might not be able to compete safely in some disciplines.
* Horses that are unhandled or unsafe: Horses need to be trained and safe to handle before they can participate in a show.
Ultimately, the rules for which horses can be shown vary depending on the specific show and discipline. You'll need to check the rules of the event you're interested in.