Shoes really depend on the horse. I personally don't think it's wise of the BO to require it for outside horses. I have a paint gelding that has never had a shoe near his feet and I have ridden him threw rocky mountain trails, canyons, and sheet rock/lime stone creek beds. He's never missed a step! However on the same note, my mare has great hard, black feet for most trail riding but when I tried to ride her in shoes (for a really, really rocky trail), she sliped on and tried to jump over rocks. It would have been better to leave her barefoot so that she would of paid attention to her feet and placement instead of freaking out from slipping and then trying to jump.
I say that to say, if the BO only enforces that rule for the safety of rider and horse, and IF you KNOW that your horse can handle the trails barefoot, then he should listed to you and allow you to ride sans shoes.
IMO, the boots aren't worth the money. On a hard trail, they tear up and fall off. They have been such a pain in my experience with them.
One is closer to God's heart on a horse than anywhere else on earth!