It is a bit of a how long is a piece of string question with all the possible unknown variables. You can probably find out the answer by talking with your parents, they will be funding it after all.
However what I wanted to say was please don't take on the responsibility of a horse without first knowing what you are doing. They are difficult and time consuming creatures to take care of.
Perhaps joining a pony club would be a better idea as you are taught how to care for a pony, more riding skills and there will be people around who are experienced and can catch it when you accidentally take off it's bridle in the middle of a field without putting the headcollar on first (true story).
Pony clubs are also good as you can board or just travel there every day. You can make lots of friends and take animal husbandry exams.
Would you want to put your horse through unnecessary suffering if you were just not experienced to notice it had ill fitting tack or some other disease? Also moving a horse away from it's friends to unfamiliar surroundings for a couple of months is a bit cruel as well.
You should think carefully before you do this. It's not like renting a car.
Almost forgot to mention, perhaps you could start working at the stables which you ride with at the weekends. I used to do this and it taught me a lot. It gives you a good taster of what looking after a horse actually involves.
Sometimes that is standing on top of a pile of manure in the freezing wind and rain after being running after a little watsit of a pony for the last two hours. You are tired, dirty and smelly beyond belief. Your hands will be sore from lugging bales of hay by twine and you think you might have broken your foot when the 18 hand monster stood on it and wouldn't get off. You stand the chance of being bitten, kicked and crushed against walls.
That being said some of the best fun I've ever had. But make sure you go into this with your eyes open. Horses need routine and you can't decide to have a lie in one day.
I am mostly just playing devil's advocate here, so if you have seriously thought about it, go for it they are wonderful animals. Good luck :)
here is a nice site
How to Lease a Horse