I don't want to sound cynical either, but I will tell you the same thing that my father told me when I wanted to do the horse program at Virginia Tech.
He told me that getting an Equine degree is way too specialized. If it doesn't work out, it would be hard to find a job that pays the bills. An office won't hire you for your skills with horses, that's meaningless to them. And in the same vein, if you did want to be a trainer, instructor, it doesn't seem like the people that hire for those things would even care whether you had a degree or not.
It would be much better to get a broader degree, such as business, and then you can use what you know from that to find a job involving horses, like managing a horse business. You could use a law degree to work specifically with equine law. In getting those broader degrees though, if it works out you don't make as much money as you'd like, you can use them to get a job outside of horses.
Think carefully about what it is you'd like to do with horses. Being a equine vet is most certainly a worthy goal, and would require a specialized equine degree. Other things you can think about could be manufacturing of equine goods, sales, research, construction/architecture of equine housing, etc. With those types of things, just having an Equine Science degree may not get you as far as you like.
Getting paid to do what you love (riding/training I assume), is a nice thought, but it's not realistic in most cases. Just like there's tons of girls that want to grow up and be famous hollywood actresses, there's also a ton of girls/boys that want to grow up and work with horses, so competition is fierce in such a specialized industry. That doesn't even count the people who have already "made it" and are well established in your area. And, as someone else mentioned, if you get hurt, you can't work at all. AND you have no provided health care, no 401k, no vacation, no benefits from a company, you would have to get it yourself.
I would suggest not picking an Equine major, unless you're going to be a vet. You can still work in the horse industry, but pick a major that could be used in all industries, ex. Marketing- you could join/start an ad agency that caters to Equine clients, but if that doesn't work, you could still get a job with any other marketing firm.
If you do decide not to major in Equine Science, you could just find a collge that has a riding team, or riding classes, that way you can still do what you love and learn while you study. Maybe you could use it for a minor!
Again, I don't mean to sound cynical, but I am a very practical person. It's easy to get caught up in a dream, and maybe one day you will be the professional trainer or rider you want to be. But unless you have someone else paying all your bills during and many years after college, it would be extremely hard to start up.
I want to add also:
http://diplomaguide.com/articles/Equine_Science_Masters_Degrees_Career_Info.html
This is for a Masters degree, which would require more education than a bachelors.
Average starting salary of $33,000, which is not a lot. I made that fresh out of high school with zero degree.
It's all well and good that you don't care about the money, but your horses will care when you can't afford to feed them, or keep their feet trimmed, and your car breaks down and you can't afford to fix it, or your heat/water gets shut off in your house.
I don't mean to rag on Equine Science Majors, but I highly recommend getting a more versatile degree.