Join Date: Aug 2009
Location: New South Wales, Australia
I would wait. Lessons with an instructor who is good with kids will probably go a lot further than riding around on your own horse.
It's not just the cost of a horse, and it can easily cost upwards of $1000 for a pony suitable for a child, its tack, rugs and other gear. Boarding, feed, farrier, vet, which could go into the thousands in the case of injury. Horses aren't cheap.
Your daughter may be asking to ride everyday, but when I was four what I wanted more than anything was a gorilla. But things change. At four she'll probably be starting school soon, so she may not even have the time to ride everyday. It can be good sometimes for children not to get everything they want.
Give her two lessons a week or something, and after two or three years if she is still keen then look at buying her a pony.