Equine science degrees get you almost nowhere because the equine industry is all about on-the-ground experience. Everyone I have ever met who got one still wound up working an on-the-ground type of job where hands-on experience trumps book knowledge. Unless you're going for an actual science major with a focus on equines (reproductive biology, veterinary, behavior studies), save yourself the money and just buy or rent the textbooks you would use. Services such as Chegg allow you to rent textbooks for a quarter of the cost of buying them outright.
If you want to learn to train, the best thing is to find a trainer who would be willing to take you on as an apprentice or a working student. Many big-name trainers like John Lyons have apprenticeship programs where you go do several weeks or months of intense, focused study, or work with a trainer locally who is certified. These do cost money but if you find a trainer you really like, and want the business boost of being able to claim yourself as certified, so much the better.
You can find as much information online from reading, watching videos, and reading articles for free as you would taking a course you'd have to pay for. Check out Coursera, which runs free online courses, and they have two equine courses.