And I wouln't/shouldn't get JUST that certification right? It would just be to help me as a hippotherapist, and I'd still need a degree as an OT?
There is quite a bit of controversy over the "hippotherapist" certification and the benefits of riding as a therapeutic modality.
But, to cut to the bottom line, you need to have your PT or OT degree, certification, license, and a doctor's order and approval of your plan of treatment to be reimbursed by insurance for the work you do (third party payors). There are some states that allow "direct access" to therapy, but finding a third party payor who will go along with that is rare. The "direct access" (getting a service without doctor's order) is optional and does not require third party payors to pay. They can have more stringent requirements.
Inability to bill third party payors is the biggest reason that therapeutic riding programs depend so heavily on donations and fund raising. Why they set up as non-profits and go for tax exempt status. The overhead is outrageous and the reimbursement is not there.
A degree in PT is often more useful if you are going to focus on physical disabilities with the riding. A degree in OT is often more useful if the program is going to focus on psychiatric health. Each can do the other, but if you wind up in court defending your plan of treatment or have to fight a payment denial you're education will not be questioned as harshly.
I know of a few programs that lease horses and space to PTs and OTs for specialized treatment that the therapist can bill for, while the center continues to operate their own hippotherapy program dependent on donations.