I grew up in new england with horses and riding.
Let me tell you, it's a hobby for rich people.
It will eat you up financially if your kid gets really into it.
As much as I like horses, there's no way I'm going to let my kids ride anything other than the fat ponies over at Ft. Wilderness for 3 bux a pop. The more your kid gets into riding, the more they come in contact with the "horsey set", and believe me, when your kid sees the other kids with the 1800 Hermes saddle, they're gonna want one too

. It's the equine version of the Prada bag.
Don't even get me started on the number of times I was kicked, stepped on, thrown and dragged by my stirrups. There's no way I would expose my kids to that sort of risk, either...
Try soccer; much cheaper, much better for your cardiovascular fitness and a lot less chance of a one ton prey animal going bonkers over a sheet flapping in the wind and bolting and dragging your kid down a field while you run fruitlessly behind them yelling "stop" "stop".
Been there, (as the kid) done that, have the scars.