Wow, why don't you think you could make it as a vet assistant? Are you so sure you do not want to? Many people who are a few years into college still don't know what they want to do. It is okay to be indecisive, especially at your age.
What my friend did, she went to college for equine therapy, got her bachelors, and then decided that she wants to go to vet school. She is currently in a pre vet program and is well on her way to becoming a vet.
I would suggest when you are looking into colleges several years down the road, you should look at the Kentucky Colleges. Kentucky is FULL of Race Farms very near to many of the reputable Equine Colleges. They are always looking for grooms, office help, barn help, foal watch personnell, etc. That could help you get an "In" into the racing industry. In Lexington, you could apply for a job at Keeneland, help with the sales, etc. There are many many horse related options in Kentucky.