Buying a horse or pony - starting cost for one that isn't very old and can't be ridden anymore, or that hasn't got lots of problems you definately don't want to have to deal with around a child - about $5000 minimum if you get a really cheap deal on a really common breed that has only been broken in basic, and it goes up and up and up. A well-bred well-trained mild temperament good for kids little pony can easily set you back $10,000 or more.

Leasing land in that area suitable for a horse, add a few more thousand. Buying land of sufficient size, add tens to hundreds of thousands depending on exact size and location. Building horse stables if not already on the land, up to about $10,000.

Annual veterinary bills, add a few hundred if the horse stays perfectly healthy and only needs a check up. If anything goes wrong, add thousands.

Saddles, reins, harnesses, bits, shoes, grooming gear, etc etc etc - add a few more thousand.

Food - Double your grocery bill and you'll be getting close.

Caring for a horse requires at least several hours of attention every single day. Grooming, feeding, cleaning stalls, picking up horse poop from around it's paddock, exercising, riding... it's a heck of a lot of work. After all those other costs, could you really afford to hire someone to do it all?

Leasing a horse - good luck finding such a thing! People that own horses put a lot of time and money into them and generally don't lease them out. They aren't like cars.

You might be able to find a pony club that owns horses or ponies that she can ride when she attends, but they cost a lot in fees - though not as much as owning a horse it's still not cheap - and if they have more members than they do animals, she might miss out on a lot. Most members have their own animals, but it won't hurt to ring up and ask.

Most such clubs can be found in the yellow pages under the heading "Clubs" not sure what subheading it would be under though.

I dont know about where you could lease some room though, you could look in a local paper or phone book for stables which offer public stalls.