I did the equine science. Personally? I think they're all a waste of time. It's like operating a hoe or a dozer. You won't get hired by a piece of paper, but by the experiance you have.
If you're going the horse avenue, go work at a well known barn or trainer. I learned WAY more, and got all my training people from that experiance without ever mentioning my Major.
I would go to school, but get something like a bachelor of science or go the whole nine yards to become a large animal vet,or something else that interests you because trust me, the horse industry is NOT kind to anyone who isn't a millionaire and just starting out.