Not having a car is going to be the biggest hurdle unless someone is consistently able to carpool you to the barn. How far away is the barn? Travel can suck up a lot of time. Is there any way you can get your own car?
If you can, try to schedule your classes as a block of time. This can be difficult as a freshman because you'll be the last to register, and as an upperclassman, the smaller major courses may only be offered at one or two times. Your first year will probably be a bunch of pre-req courses but you need to do well in them as architecture degrees are considered professional programs, and your performance 1st year determines whether or not you'll be admitted (not sure if this is the case at your university). Architecture degrees are time-consuming as you will have a lot of projects and studio classes.
More practical advice, get to the gym while at school. Riding, especially at the level you're wanting to do, will be a lot easier if you're fit. Not saying you're not, but if you do end up needing to take a break, you'll come back to your previous skill much quicker if you stay in shape. Pilates is great for equestrians but anything you enjoy will do.
You can always work at the barn and show during holidays and summer breaks, but eventually you'll want to do an internship in your junior/senior summer. Make school and your future career your first priority, horses will always be there. (above advice is assuming this is a bachelor's degree; I'm not sure about the difficulty/flexibility of an associate's)
Showers Off and On
