Once upon a time my mom, who has extensive experience in business, human resources, payroll, etc. was contemplating potentially opening up a boarding barn one day when she retired. Then she started coming to my riding lessons and began chatting with the B/O about all that goes into it, and just observing what was going on, and she realized that, unless she spent the next several years really working with and around horses, she would be way in over her head if she just jumped into it with her business degree and a few courses in equine studies offered by one of our local universities. So she scratched that idea (and probably for the best, although my young self was kind of bummed).
No degree, even a PhD, could ever compare to experience and "work in the field". This includes opening up a boarding barn for horses. While these things will definitely help you in managing your business, they will not help you with the day-to-day things that build up and the weird (but very common) problems that happen when it comes to horses and running boarding barns. In addition to equine studies, I would also recommend taking courses in veterinary technology (specializing in equine if you can find a course), equine nutrition, equine behavior, agricultural management, etc. if you are really serious about additional "lecture" courses and information courses. But again, no amount of certifications, degrees, CE credits, etc. will take the place of good 'ol experience.
For example, I own my own dog training business. I have a single certification and a degree and am not registered with other dog training organizations, but I have over a decade of experience working with thousands of different types, breeds, personalities, and behavioral issues...from shelter dogs to service dogs to aggression cases, etc. I spent about five years interning under an dog behaviorist at our state's largest animal shelter while I was working on my degree. There are several other dog trainers in my area, all of whom have this and that degree and certification. They advertise their businesses as such and I don't advertise at all (I get clients through word of mouth). Usually, I have a waiting list at least a month out (if not more) for clients who tried the other trainers first and realized that those trainers couldn't help them or their dogs with their training because those trainers use "cookie cutter" techniques they learned in their certification and educational courses rather than go off of experience in previous training cases they had through the years and cater to each client's individual wants and needs and adjust as new scenarios and problems arise, as I do in my training courses.
If you are serious about opening a boarding barn, start volunteering (or better yet, see if you can get a working student position) at a local barn to really get involved with horse care and management "at the ground level". Take riding lessons, too, if you aren't already (you didn't state what your horse experience is). Go ahead and take some certification courses and if you have the time, money, and energy you can get that degree in Equine Studies as well, but again experience is where it counts in this type of situation. Boarders want a barn where the B/O is calm and collected at all times...not running around like a chicken with their head cut off if something pops up that their university course didn't cover.
Good luck! :)