How to persuade parents to get a horse ?

Tough

You are a child and can't afford the horse or its vet, food and boarding bills. If you had done your research like you claim then you woudl know that horses are very expesnive to maintain but you clearly haven't since you expect mummy and daddy to pay 3-600 a month for YOUR horse

You can get a job, save up for a few years and then get one. Can't? Then tough.

A horse is 1,000+ and the boarding is another 2-300 a month and food is another 200 a month and that is not including any vet bills

Since you expect your panrts to pay for all of it you can wait until you get a job

Horses are expensive. Between food, shelter, medical care, and other expenses it can run you thousands of dollars per year, not to mention the initial cost of purchasing one.

Then there is the work: they have to be fed and watered daily, feces has to be collected, sawdust has to be cleaned and replaced, they have to be exercised and groomed, etc.

Honestly, I can understand why a parent would be hesitant; On top of the financial burden it would place on them, they would probably have to do the work themselves. Would you really be willing to spend time every day doing manual labor? Would you be willing to do that work for 10+ years? The horse will still be alive long after the thrill of getting a new pet wears off.