Persuading your parents to buy you a horse when the answer is "NO" is definetly a difficult task, but the strategy you must keep in mind is: PERSISTANCE. Persistance is the key to obtaining. By now you might have realised that your parents can be stubborn. But you must also keep in mind, that your parents may have genuine reasons for not being able to keep a horse. For example, you must understand that if your parents are not particularly wealthy, you may not be able to afford a horse. Hence the expression "Poverty is owning a horse!"

But then you have the parents that can afford a horse but won't get you one.  WHAT CAN YOU DO?!

As mentioned before, you must persist! At no costs must you become quiet! You must constantly hint and hint and hint.
Hint about what kind of horse you want, what you want to do with it, what kind of saddle you want, how much you want a horse. AGAIN, REMEMBER, do not die off the hinting! YOU MUST PERSIST!

OK, you've been hinting and everything for a long time now, it's time to show your parents that you ARE dedicated and passionate!
Ask your mum/dad to watch your riding lessons. Then get off and ask, "how did I look?" ask your parents to hold the horse while you run and do *something*. Have your parents around while you groom the horse (that's if you can) and bluntly, show off your horse knowledge...show them that you know what you're talking about. For example, while you are picking out the horse's hoof, say

"See this here, mum, this is the frog. The frog is probably the most delicate part of the hoof (other than the nerves ofcourse). When you pick out the hoof, you have to be really carefully not to bump it, because if it gets bruised then there can be trouble. As the saying goes 'For the sake of the nail, the shoe was lost, for the sake of the shoe the hoof was lost, for the sake of the hoof, the horse was lost'" and in other words ramble on and on and on.

Get your parents involved with your riding. Get them interested and wanting to know more. Share interesting facts with them etc.
Get your parents to buy you a grooming kit for your birthday, then upgrade to buying a saddle-cloth, then a halter and leadrope etc. and slowly accumulate the necessary needs for owning a horse. (That way you can say when you ask for a horse, I've got almost everything I need for my horse that way it won't cost as much)

Now's where you get ready for the main 'battle'. Die off the pleading and hinting for a little while (a couple of weeks) and then you come down hard. Well, I'll tell you what I did just to give you an idea. I wrote a ten page letter, consisting of things about how much I'd want a horse, how much it would cost (try and make it sound as cheap as possible- all you need is the go ahead and then you can break the news that it might cost more!), that you don't  need much gear, how much time it would take (try and make it sound appealing ie. not that much time) how much you want a horse, and if you go to UNI, that you won't be able to get a horse for a long time, and that the childhood years are meant to be the best years of your life and how much more enjoyable it would be with a horse. OK, now comes the pleading. I wrote two pages of "PLEASE". Then after writing this, I left it in an evelope on the coffee table with two cups of coffee (for my parents) and left all my books open on 'first horse' sections. Your parents are bound to come and talk to you (probably saying sorry but no) that's when you turn on the waterworks (crying). Just say you've wanted it all your life and you probably wouldn't have a horse all your life and how much you want it, how everyone is getting a horse except you, that you have all this gear and you believe you're ready to upgrade from the school horses. Mention that you'll most probably have to get rid of your horse for the tough years of high school (though, you will have to tackle this hurdle when the time comes) Anyway, they'll soon get the picture (you have better arguments than them too!) then leave them...and hopefully they'll discuss.
Anyway, I did this and it worked!

All you have to do is persist. What I mentioned above may not always work in different situations. There mayl be legitimate reasons as to why you can't have a horse and there is no use getting angry at your parents for this. If that is the case try and find out ways that you can get a horse. (These will vary from situation to situation) If you would like further advice on convincing your parents, why don't you: