What is "pretty deep"?
If this is like most such horseback deals, you're going to be riding on the beach and the guide will tell you "Okay, anyone who wants to can take your horses into the water here ..." thus leaving it up to the individual rider. They'll pick a spot where there's little wave action and a smooth bottom because they're catering to people who -- like your 11 y.o. -- has anywhere from zero to tons of horse-riding experience. And apart from not wanting you to get hurt, they also don't want to risk their own horses.
And frankly, a kid with zero horse experience is going to be given a horse that will do little but plod along. I doubt he'd be able to get the thing to a trot if he wanted to, let alone frollicking in the surf.