When I was a teen, I owned horses. In fact, I owned them for awhile after I got married. As with all things from my youth, though, I gave them up in favor of raising children. Still, we wound up with horses again for awhile when the children were young.
Horses can be fun and can open up your child to opportunities for competitions where they can earn trophies, plaques, and even a few dollars. Naturally, your expense will come from purchasing the horse, tack, and horse riding apparel to begin with, but the rewards of horse ownership cannot be questioned if you have the right animal.
The responsibilities of horse ownership for your child can develop in him or her a responsible outlook later in life. A horse is entirely dependent upon the owner for food, water, shelter, and even protection. As large as they are, they need these things from the owner or they don't do well. In return, they give you friendship and entertainment. The investment in time is paid off well when your horse perks up upon seeing you coming.