Private clubs can enforce standards of behaviour even outside their club. The rider is the one being tyrannical over a little pony. The club (FEI) is well within their powers to declare that behaviour not in keeping with their club’s standards and banning him from membership.
(Similar to trainers who killed horses for insurance money, or trainers who sexually assaulted people).
I know I don’t want to compete against people who use horrific training practices, and I don’t think this is the image we want our sport to have.