How can i convince my parents to let me have a horse?

The thing is, your parents are right. Horses are a lot of money and I mean a lot. That 1500 in USD is barely going to cover anything. Horses can cost up to thousands of dollars in a year. Right now, they are putting out a lot of money towards your volleyball and while dropping volleyball would help, it wouldn't only be minimal. I would suggest continuing to ride at your grandfather's place while you save up money. Perhaps, have your parent's instead of putting the money towards volleyball they can set aside an account for you to save up for a horse.