I’d move.
Let’s say you do lock them in. You’ve already said these kids are throwing rocks at the horses. You’re on a military base. I’d worry about my horses being unable to get away from a harassing kid. Or poison in the only source of water. Or a million other things that could go wrong. (Granted, the same situations happen in a paddock, or if the horse gets loose, etc.) I’d also think the lock may “challenge” the kids and they’d target that horse, thinking it may have a higher value/meaning/etc.
If not, security guard all the way.