Unfortunately horses are very expensive animals. You buy the horse but then you have to buy tack, feed, vet care, ect. BUT if you have the will you can find a way ;) I know I'm eating ramen noodles all year so I can afford to take some horses to arabian nationals in 2011 (and don't even get me STARTED on how expensive THAT is). ;)
The others have given you some good ideas. Maybe your parents can pay for at least half? Or you could ask for money for your birthday/other holidays for lessons.
Every great dream begins with a dreamer. Always remember, you have within you the strength, the patience, and the passion to reach for the stars to change the world. ~Harriet Tubman