@Charles4515, thanks! I was originally thinking about going around 9:00 a.m. and thought that was early but if Watson's will do a ride that early, I'm there! That way I'll have more time to go see other places I was planning to visit.
OP, the website does mention you can gallop but also says minimum age for children is 9 but maybe if you explain they compete they might make an exception. If you do go and it's before July, maybe you can post about the experience!