I was lucky my daughter learned that owning a horse cost more than purchasing one, as is with ALL animals. It's not the cost of the animal but the care & maintenance. Vet bills are the hardest to deal with.
howfunkyisurchicken makes a very good suggestion with your parents approval......
Volunteer to help out with barn chores at a neighbor or family members farm, or perhaps do some research to see if there are any horse rescues in your area. Not only would you get your horse fix, but you'd be helping out your community and the animals that live in it.
What my daughter did was volunteer to clean stables, she went every day during the summer (I drove her) 7 days a week, no matter what the weather conditions were. She got noticed for her dedication, in a short time some of the owners allowed her to exercise their horses in the area, take their horses out on the trails. They coached her & taught her, she learned. Once school started after homework, back to the stables and this went on for couple of years.
At one point she was then entrusted with the care of a pregnant mare, unfortunately was in school when she gave birth but then had the foal & mare to care for. Few months later the owner decided to sell the mare & foal, it was the last time she went to the stables. We did drive up to the property the pair went to, it was beautiful pasture and my daughter was good.
When we moved to San Diego, she found a small outfit that gave trail rides, took her to check it out and she volunteered to clean stables. They took her up on it, again I drove her (50mi each way) everyday. The owner then invited her to go on trail rides to help out, she had a blast. But one thing she did learn it's very expensive owning a horse, she learned RESPONSIBILITY.