Well there are a few things wrong with the entire thought process. I'll break it down for you this way...
It's great that you have a goal, but since you only havea year until you work, you may want to wait. And even then, this might be too expensive to get into.
Even if you were able to find free board, you realize that the cost of a horse is anywhere from $100-$500 a month right? Farrier, vet bills, feed, hay, shavings, tack, etc. Just wanted to make sure you don't jump on $70 board and then realize you don't have the money to care for the horse.
The other half of this is about the lease situation. 1) You don't know if the leasee and horse would bea good fit, because you don't know the horse you'll be leasing yet. 2) Even if you found someone willing to go in on this with you, what would you do if THEY decided to back out? You'd be stuck and responsible for 100% of the fees assosicated with the horse.
Leases should be used as additional income towards your horses care, but never as the income for your horses care. You have to be able to take this on yourself before you decide to purchase.
Hold off and take some lessons. $70/mo should get you 2 lessons a month. Start there. Owning a horse is a huge financial responsibility and strain for an adult. Being a teenager and trying to conquor this is almost impossible. I'm not saying it is impossible, but every last cent you make would go to your horse.
Just keep an open mind about how realistic this goal is... right now anyway.