When I was 12 I started to volunteer at the stable I work at now. I didn't make money right away, but I learned so much about horses that it was worth it. After about a year, I was getting payed minimum wage. Eventually, I got raises thorough out the years. The plus side to working at a stable is that you may be able to ride/exercise horses for free. You also may be able to get free or reduced board, so when you do get a horse it'll be a little easier on your wallet in the long run. You might be able to get good deals on horses for sale, since you work there/they know you.
There's a boy at my stable right now that's 12 and getting payed $20 every 8 hours. Our barn owner doesn't mind having preteens/teenagers working there because they've made the best/most loyal workers for her.
Also, if you start working/volunteering at a stable you might be able to go to auctions where horses are going for $50-$75, so buying the horse might not even be the most expensive thing if that's the case.
For what I pay yearly...
Teeth floated once a year - average $100
Shoes every 6 weeks - $95
Wormer every other month - average $10
Spring shots - $85
I pay board on Athena, so I don't have a price on grain, hay, or shavings for her.
Teeth - Average $100
Trim every six wks - $30
Wormer - average $10
Shots - $85
Joint supplements - $40 every month
Hay - $60 every month or so
Grain - $10 every other month (he barely gets any)
Shavings - $5 for two large garbage bags every other week or so
Every horse is different, and depending where you live, prices may vary. Some horses go barefoot, but you might find one that needs special shoes which cost even more then regular ones.
I used to only pay $15 for a trim, and $30 for shoes all around. Now it's $30/trim and $95/shoes all around.
If you buy an older horse you may have to pay more for special feed or supplements, too.
I also already own all the tack I need for them, so you may have to spend more if you still need to get saddles, brushes, etc.
The biggest problem for you right now would be driving. Someone would have to drive you back and fourth if you did find a job.
If I were you, I would try and find a stable that would be willing to let me volunteer. Most stables, at least the stables around here, won't hire just anybody with horse experience, you'd have an advantage because you'd know what they like/how they do things etc.
This is just what I did when I was your age, but I'm sure you could find some sort of odd job that can make you some moo-la if you're not sure about working at a stable.