I'm often asked how I got my degree and where others can go to get a degree in equine behavior. I don't know of any schools that offer a Masters or Doctorate of Equine Behavior. You'll actually be getting your degree through another department, likely Animal Science, Equine Science or Veterinary Medicine. You'll want to pick a school that has an ethology section, an equine section with a professor/advisor who is interested in behavior or a behavior section. My degree is in Animal Science, obtained through the ethology section. I chose to focus my research on equines. My Masters' thesis was on imprint training and my doctoral dissertation was on clicker training. I took classes in ethology and immunology, in agriculture education and in learning (through the psychology department). The combination of my research, class work and previous experience working with my own horses and for various trainers gave me the background to become an equine behaviorist.
Before traveling down this road, I advise you to consider what you what to do with your degree and training. If you would like to work in academia, teaching classes and doing continued research on equine behavior, then you'll want to go to a university that has a strong research program and publishers papers in scientific journals (Applied Animal Behaviour Science, Equine Veterinary Journal, Journal of Equine Veterinary Science, etc.) and one that presents data to scientific conferences. You might look at Pubmed (www.pubmed.com) for research that interests you and contact the person doing the research.
If you would like to become a veterinary behaviorist, one who treats animals for physical as well as behavioral issues, you'll need to go to veterinary school and take behavior classes. If you want to become a practicing behaviorist (one who takes on clients and works on behavioral issues), you need to know that it is a tough job to get started in and does not pay well.
You might check out the Animal Behavior Society, International Society of Applied Ethologists, Equine Science Society, and Equine Nutrition and Physiology Society. I don't know anyone in your area specifically to refer you to.