In our area, there are a number of small towns that have rodeos once or twice a year. All you have to do is show up and register by the deadline...unless you want to ride the roughstock. If you want to ride the roughstock, you have to pre-register.
We've joined a local "round up club" that has a lot of horse related games and activities - including an annual rodeo. We have "playdays" nearly every weekend when school is out, and a big poker run/trail ride every fall.