I've been on a drill team for the last 4 years. And about the rodeo- yes they are a good place to get a horse ready for an actual show, but you will have to talk to the director of the committee running the rodeo if it is okay to bring your horse. Some will, some won't.
Just remember, before you start hauling your horse to shows, you have to have him ready. You don't want to go to the show trying to make an impression, because there may be drill team members there, and if your horse spooks at something you don't want to make a bad impression.
About your horse- you need to be sure he is well-broke. He needs to be able to walk, trot, lope, and run smoothly, with smooth transitions. The stop is also a major factor, as well as the back. He should also be able to pivot on the front and back, both directions. He also needs to be able to lope a perfect circle for fans, crossovers, etc. He needs to get along well with other horses to, and be able to carry flags. A horse that travels well is also a bonus.
After you have all that, start taking your horse to events. If you think he is going to be spooky, bring a friend with a good horse that your horse can follow.
If you want a good one to look up. Youtube the All American Cowgirl Chicks and the Latigo N Lace drill teams. They are both really good. Just remember you probably won't be doing much trick riding; just depends on the drill team. And if you want to, don't be scared to call the drill team coach and see what they look for and what they need. If your team doesn't have sponsors, it can get pretty expensive if you have to buy your own uniforms, protective boots, gear, and pay your part of fuel and trailers.
It is a lot of hard work, but don't give up. The drill teams are very fun, and it is great when you do a perfect performance and are signing autographs and taking pictures with fans. Good luck!!