A few considerations:
-Who will be paying for your board and lessons? If it's you, you'll need to pick up a part-time job to pay those bills. This will potentially cut into your riding time in a way that wouldn't happen if you just stuck to lessons or a part-board.
-How often will you, realistically, get to ride? I owned a horse at your age and only made it out to ride twice a week, as I was dependent on my busy family to drop me off and pick me up. In hindsight I would have done better to stick to lessons or a partboard. If you won't get to ride more often than you do now, the only major difference will be quadrupling (or more) your monthly horse-related bills.
-Who will pay for the vet if a veterinary problem arises? If you're just taking lessons or part-boarding, the owner will be on the hook for those bills, and the farrier bills -- not you.
-If the horse injures itself in a way that requires daily attention, debriding proud flesh, changing bandages, etc., will you be able to get out there every day and take on that responsibility?
-If you buy now, you likely need to plan to sell your horse before you attend college -- if you plan to attend college. But what happens it, by the time you're ready for college, your horse is unsellable due to lameness or an injury? You could be faced with the decision to put down a horse for financial reasons, which happens, but is very hard on a person's conscience. (I speak from experience.)
I'm 36 now and don't own a horse because, looking at the bigger picture, I already have more opportunities to ride than I actually have time for. I could take multiple lessons a week if I wanted to (and had time!) and get much more constructive experience from my rides and STILL not have it come even close to what it would cost to own a horse. Owning a horse would actually cut into my learning opportunities regarding riding. The prospect of vet bills, sudden lameness, etc., aren't my problems to deal with, and that is HUGE. I also know enough people with horses who WANT them ridden that I do a lot of riding for free. If you continue to advance and learn and treat everyone respectfully, opportunities to ride have a way of making themselves available! You could also volunteer to do chores at the stable in exchange for non-lesson riding time, and it would be darn close to having your own without all the bigger-picture hassle and expense.
Alllll that said, I totally get the impulse. I window-shop horse and pony ads CONSTANTLY and am often glad I don't have a bunch of money to hand right now because I'm not confident in my self-restraint.