Absolutely you need to be very careful in placing a horse in a college or therapeutic riding program - just as much as if you were to sell the horse privately. Ultimately, when you give up ownership of a horse you give up control of its outcome, and unfortunately many horses are going to wind up in less quality homes as they age, have less athletic ability, etc.
In my opinion, if you truly care about the horse’s well-being, the best thing you can do is remain in touch with the school, therapeutic riding center, or private seller, and keep up with the horse. There are places where the horse will get fantastic care, and places where it won’t, and circumstances in a school or nonprofit can change drastically over the years.
I’m on the board of a therapeutic riding center, and we take, IMO, exceptional care of our horses. They live on beautiful pasture, carry a light workload, get supplements and maintenance as needed, see a vet and farrier religiously, get chiropractic and acupuncture, etc. When a horse is ready to retire from our program, we make every effort to find them a good retirement home, often with volunteers, and/or return them to their prior owners. However, please be aware that from a nonprofit’s perspective, the organization has a fiduciary duty to use donated funds to fulfill the mission of the organization. In the case of our organization and many others, that mission is to offer equine-assisted activities and therapies to children with disabilities. It would be unethical for us to take donations toward that mission and use them to feed 10 retired horses. We regard our horses as equine staff, and we care for them to the absolute best of our ability. We appreciate what they do, and our program could not exist without them. However, we must direct our efforts to providing the best possible therapeutic experience for our clients, not toward providing a cushy retirement for our horses. Riding centers should not be construed as retirement farms - sorry to be on a soapbox, but this is a pet peeve of mine as I think much of the horse community has come to regard therapeutic riding centers as a great place to rehome elderly, unsound horses, which we just are not. Our horses work hard - they deal with tantrums, unbalanced riders, rider miscues, medical equipment, etc - while often older horses retired from showing or needing a stepdown career are perfectly suited to this work, asking a horse with soundness issues to carry an unbalanced rider is just not right in my opinion. I don’t mean to imply that we don’t take care of our horses - I’ve been out at the farm multiple times just in the past week to provide extra care to two horses who were injured in the pasture. However, they get care as equine staff members, not as my personal “pet” horses - they are going to get good basic care to keep them sound and healthy, but the program is unlikely to be able to invest money in extensive diagnostics, colic surgery, etc. I think anywhere that you are placing your beloved horse is worthy of some time researching, checking references, etc.