I am waay older than you (38), but I bought a horse when I was 16 and kept him until he died when I was 28. I had him through high school, college, many jobs and then my first "real" job as an RN. I had him through two long term boyfriends and a marriage. He and I went through a lot together. This is my long story, and also how I was able to keep him paying for most everything by myself.
I see other people have left ideas too on how to keep costs down. First of all, I learned to do his feet myself, and of course he went barefoot. He had great feet, but we still had to watch where we rode (I am primarily a trail rider), really rocky areas did not seem to hurt him but they tore his feet up. In high school, I simply worked part time and payed for his board. Easy enough. College, not so easy. I was unable to work when school was in session. I had a full load of classes, and the nursing program I was trying for was highly competitive. You basically had to have a 4.0 GPA to get in. I tried to work and commute and keep my grades up, could not do it, I could only work during the summers and that was not enough money for a horse. What to do....
I had a friend who had a horse too and was going away for college, while I lived with my parents and went to the local university. Her parents had her horse on their property and told her she could keep it, and they would pay for hay and everything, but there was no way they were going to take care of the horse while she was away. That is where me and my horse came in. I moved him over to her parent's place when I was 18. All through college, I fed and cared for her horse as well as my own. The best thing was that 9 months out of the year, not only did I not have to pay board, but her parents payed for all the hay for both our horses. When my friend was home for the summers and took care of our horses, I payed like $90 a month for feed and board. When the hay was getting low, or I needed a check for her horse's farrier or wormer or vet, I just left her dad a note, and he would leave me a check or call and order hay. During the summers my friend and I would go to the lumber yard and get shavings for the year in her dad's old truck. It was like we had our own little stable, and everyone was happy. I got to keep my horse, she got to keep hers, and her parents just wrote the checks, which they could more than afford to do. I seriously lucked out. My parents could not have afforded that and we did not live on acreage.
Things changed when I turned 21. I got married. The same summer, my friend decided to sell her mare to help finance vet school, and she moved to the UK. I left my parents and went to live in the city with my new husband, but I still had a year left of nursing school. Money was tight, I needed a solution. Through sheer kismet I guess, I saw an ad for local riding lessons near where we were living and called it. I did not know any horse people where we were living, and I needed connections. We were in a suburban area, but a few small spots of acreage remained, and there were a few horses here and there near where we had our apartment. I just told the woman I was new to the area and looking for a rough board situation for my horse. She said she did not know of any, but would call if she found one, I thought I would never hear from her again.
Two days later, she called me. She had gone to purchase a used saddle from an elderly man who had a two stall barn and small pasture empty that he was willing to rent out. I was back in business. He only charged me $45 a month rent, I bought everything and cared for my horse, soon to be two horses (I got another one to keep him company, she was free), twice daily. After struggling through that last year of school, I finally got my first real job, and felt like I was rolling in it. The first thing I did was buy a truck and trailer so we could go to trails as there were none close by, and we went everywhere I could think of, and had a blast. That lasted about 7 years total until we could afford our own place and I could finally bring, my boy home.
The day we closed Escrow on the house, I had to have him put down from complications of Cushings syndrome (severe laminitis). I never did get to bring my boy home, after all those years. The old mare I had gotten to keep him company did come home with us. She lived to be 35.
The point of my long story is, you never know where life will take you and what oppurtunities will be afforded to you. Sometimes though, you may get into a serious vet bill bind, and if that is true, often mom and dad are the only way out. My horse needed major surgery when I was 19, and my parents put in $1200 to help, and the wonderful docs at UC Davis took pity on me, a poor college student, and kept costs to the bare minimum. I had to take out student loans to help pay for college, but because I chose a local University, they were not hard to pay back once I graduated, and I picked a field of work where the pay is good and the demand was high, I had my job offer before I even graduated.
It can be done. With some luck, love and help. You may have to lease your horse out for a while, I considered that because I did not know if I would get into a local nursing school or not, thank goodness I did and did not have to leave town. But I believe you can do it. Having a horse when you are young is a wonderful experience. I would have missed out on so many rides and so many friends, and so many moments, if I had not had him. Good luck....and when the going gets tough, just remember, it will pass, things will get better and work out somehow. Maybe not exactly as you had planned, but they will work out.