Welcome to the forum! :)
As Avna said, check out local stables (including fairgrounds, race barns, etc.) and offer up your services to muck stalls, clean tack, turn out horses, etc. You can gain a lot of experience just starting there and observing what goes on around you and talking to people. From there you can move on to grooming horses and maybe lunging and doing light riding for a few. It will probably be several years before you will be able to offer up your services as a horse trainer. I would actually wait to begin putting yourself out there as a trainer until you graduate from college. You are definitely on the right path to becoming one by majoring in Equine Science, though! You will gain a TON of experience and knowledge through the classes you will take and when you finish you will be a step above your competition.
You may luck out and find a barn who is willing to exchange you working around the barn in exchange for some riding lessons, too! I did that when I was younger and it really started me off on the right foot with horse care and learning how to work with them on the ground, especially at feeding time and during turnout which you don't always get to do if you are just taking riding lessons on a lesson horse.