There are some rental car companies out here that let 18+ cadets rent at a discounted rate and drop cars off on base, although I'm sure there's some limit to how far you can take the car away from the Springs. I know a lot of cadets have used rentals to get to the mountains, Denver, etc, on long weekends. I actually think it's a pretty good deal.
The issue you're going to run into is extended driving regulations the Academy has. If you're driving alone, you can't drive more than 8 hours a day, and it's not much more if you're driving with one or more other people. Driving to Alabama (20-ish hours, right?) would probably take three days or so, not to mention the costs of gas/lodging along the way. At that point, you'll spend half your break driving, and probably would still spend a ton of money.
You can get in some pretty serious trouble if you violate the extended driving limits and are in an accident-I've seen it happen here. Let me know if any of this doesn't make sense or if I can provide more information.