We had the same situation with our daughter -only she is 4. We were skeptical that any place would start lessons that young, but they did! It was dependent on her maturity level.
We go to North Dallas Equestrian center in Mckinney. It's close to the Mckinney airport. We train with a lady named Charlena and our daughter ABSOLUTELY loves it! Each lesson is $45 -and you can choose how often you go. No contracts, no start up fee, nothing. They even have a helmet and saddle that is community use. (we purchased a helmet due to sanitary reasons) All the trainers are great and Derek -the owner is super nice! Great place for b-day parties too!
Check it out:
www.dallasequestrian.com
Hope this helps!