Anyone can show a mini!
Unicorner Farm hosted a fun show in a few years ago. It was named the "Winter Woolly" and exhibitors were encouraged not to clip their horses.
One of the unique classes was a blindfolded obstacle class. The exhibitor of the horse was blindfolded and another helper could use verbal directions to lead the handler and mini through an obstacle class.
Here are some other classes that are offered at most miniature horse shows: