I think 4-H is a good place to start at this age. They can learn about horses for a couple years and decide if they still wish to ride. The great part is they can compete in all other aspects of 4-H, not just horses. There's arts and crafts, cooking, poultry shows, and all sorts of other projects. I know in my county you only have to be a part of one club and you can compete in any project you want.
4-H also doesn't typically cost a lot of money. I know there are monthly or yearly club dues, but they are usually more than affordable (Our club is $12 a year) and this covers trips, t-shirts, or any fundraisers we wish to do over the year. You'll also be able to speak with other parents about owning and caring for horses, as well as the best barns for taking lessons.
I had a wonderful time in 4-H and it taught me so many valuable lessons. I'm now the assistant leader of our club with my mom, who is the leader.
