Apparently there were difficulties implementing Horse Riding Mentoring interactions (likely because it's a living Sim, not an object), but you can give/attend free Lectures and give/attend Classes via the Hobby Whiteboard for a more "theory-based" learning experience. (Note: Classes will ask you to Mentor Sims during them, likely as a Customer too, so I think the code was copy-pasted across skills. You can ignore that task, do the Lecture part and the various social tasks and still get paid. Might be harder to get Gold though.)
Additionally, if you use Care for Animals/Care for Ranch Animals Business activities, then Customers can also gain Horse Riding skill via caring for/socialising with Horses on the lot, if they need it. This also helps keep multiple animals happy at once. For the Horse Skills, you can use the Horses Play and Learn Business Activity to encourage ball/obstacle use.