EAP
I’m doing my thesis in EAP. I’m a masters-level student, and when I’m all done sitting for tests, I’ll be a Licensed Mental Health Counselor (LMHC). Look into those programs, too. There is question right now about the future of the new degree in New York, but the policy makers in Albany are working to fix the wee small problem of the scope of practice description that clearly implies, but does not say, “diagnose”. I’m not worried, and neither is my program’s director. It doesn’t mean we can’t work right now, it just means someone else has to sign off on treatment plans, which is annoying and redundant when we have the perfectly sufficient training 
I did my undergrad in neuroscience, and minored in psych. My program has minimal requisits for entry- beyond having a bachelors in SOMETHING, they just want to see a few psych classes (intro, abnormal, stats). It creates a beautiful diversity 
Anyway, I’m no expert, but I’ve learned a lot through my readings, and in my very humble opinion, EAGALA has the best model in that it is nearly manualized (or so it seems) and has the most research of the very scant research available. I do not support mounted EAP programs (which actually aren’t EAP, they’re like Equine Facilitated Therapy)- their personal gains, while undeniable, do not promote the same growth that unmounted counseling does. Part of EAGALA’s certification process is that you first be a licensed practitioner, then you join them. MFT, CSW, MHC all fit the bill, at the masters level.
Side note, I believe “EAP” applies to a specific approach under the general umbrella of “using horses in mental health”. Kinda like saying “riding hunters” under the general umbrella of “English riding”. Hunters may have the same end goal of Jumpers in that we both want to get over the fences while on a horse, but we sure do it in quite different ways!
EAP draws a lot from gestalt therapy, some rational-emotive therapies, a bit of psychoanalysis. It is my understanding you need to be able to know about these therapies in the basic talk-therapy context (individual AND group!) before you can really hope to apply them in a non-traditional setting. Many papers suggest that EAP works best as an augment to talk therapy, and in fact there is a large talk-therapy component to the EAP session. There is usually a “check-in” to start (how are you, review from last week, follow up on homework), that week’s exercise (which may be the same as last weeks, if the client was unsuccessful in teh goal), and then processing the experience. Actually, the session is filled with reflections, questions, etc, just like regular talk-therapy… the conversation is usually just centered around what’s going on between the horse, client, and possibly the therapist. But the end is a concerted “let’s talk to each other” exchange, and it may not even occur in the presence of the horse.
Anyway, focus on becoming an excellent counselor, first, and then worry about incorporating EAP into your education. Through your internships you may be able to gain exposure, but I would suggest being patient and focus on your “office/clinic” skills, as they will be your bread and butter, no matter what you do or where you go.
Volunteering for hippotherapy programs and the like is always an excellent thing to do, but professionally speaking, you’ll get farther with being in environments with emotionally disturbed people, or other mental health clients on your resume, as EAP has a lot more to do with that than working with the disabled.
At least in my very humble, still learning, experience.
