I lived in Colorado when a kid who was permanently injured in upper level skiing sued once he turned 18, and the court ruled that the parents couldn’t waive liability for their child… In this case the mother signed the waiver, so the son and his father sued when the son turned 18.
This citation talks about this case in Colorado, and other cases, that also said a parent can’t waive the liability for a child, and the child can sue when they reach 18 or the age of majority in that state.
http://mason.gmu.edu/~jkozlows/waivkid.html
Colorado later passed legislation allowing waivers for children.
The implications of a case over liability waivers, and ruling that a parent can’t sign away liability for a child can be long reaching too. If a parent’s waiver isn’t legal, then every permission slip, or waiver is invalid if the child decides to sue when they hit 18, for an injury, a medical procedure, or a bad outcome for something the parent signed a consent for.
In the current case, I think that the fault lies with whoever decided to put the kid on the horse at that time. I see no liability for the seller, but I wouldn’t be surprised if everyone was sued, since you can try to sue anybody.