Our riding instructor has this policy for kids who want a horse. She wants them to lease from her first, AFTER they are old enough to work off part of the lease so they have to earn it. She has chores around the farm that the kids can do to help pay for their lease, and they have to learn about all the responsibilities involved in owning a horse. Then she really encourages the parents to be taking lessons or helping out also so they also know the needs of horses. She feels very strongly about not buying a horse for a kid until the kid can help take care of it (both with a time commitment and financial help).
Even for her adult students who want to buy a horse, she asks them to do a 2 week barn duty to see just how much barn cleaning is involved, not to mention everything else.
Granted, all of this is for people who want a new horse, and don't already own one. She's also shares her ledger for one horse as far as bills go. That's a scary experience! It's a tally of a years worth of expenses, minus hay which they grow and harvest themselves. It includes her lessons on the horse, vet, farrier, and vaccines, blankets, supplements, grain, etc. She just hands you a copy and lets you look at it.
I love that she has my daughter convinced that she has to wait a few more years because she has to be able to help out financially and with her time. She knows we will get a horse, but we're in no rush.