and it's not a real thrilling ride. The horses and ponies at The Outpost all look gentle and there are a couple fairly small ones -- so I'm guessing some pretty "shrimpy" nine-year-olds actually do ride occasionally. (read whatever you want to into that statement re: rider's age versus size).
I also think I remember seeing TO riders wearing helmets ( as a horse-owner, I want to stress EVEN the gentlest, kindest, best horse in the world can still put a serious hurtin' on you under the wrong circumstances -- ie: something as ridiculous as a stray paper cup or plastic bag can sometimes scare them into bolting).
Assuming helmets ARE provided, I'd give it a shot and see if you can get on a trail ride. If not, there are always the pony rides at the corrals down by Trail's End and Hoopty-Doo -- another highly viable option for kid-equine bonding.
Hope this helps.