small children on full size horses. Keep in mind, I have no experience with this please.
I don't understand how anyone is supposed to learn proper techniques when the equipment they are learning on is too big for them. In this case, the horse. When we take part in a sport, we use equipment suitable for our size, weight and skill level. So, as a small beginner, I would use a small, calm horse. Not necessarily a pony, but a very small horse. A large beginner would use a larger, calm horse. The more experience and knowledge we get, increases the variety of sizes, temperaments and skill level of the horses that are suitable.
If I compare this to skiing: ski length should be appropriate to the height of the skier, regardless of age. Ski shape should be appropriate to skill level and style and terrain. There is no way I would ever put a 4 foot tall person on the same ski as a 6 foot tall person if they are both at the same skill level (ie. Not expert).
So, tell me please -- how does it work to put such a tiny person on a horse that, to me, looks far too large for the rider?
I don't think the ski analogy works really.
My now seven year old son started riding when he could sit, and his last pony was a 12hh welsh cross. He joined pony club when he was 4 and came off lead rein when he was five. His legs only got past the saddle when he hit six and a half, partly because he's small, and mainly because the pony was round!
The point I'm making is that whatever size the equine, a small child won't be able to get his or her legs to 'wrap around' as us adults do. In the UK it's extremely rare to see kids on horses, and the pony club world is stuffed with little round ponies. However, I have observed that in North America a lot of children ride larger horses perfectly competently. I think part of the reason is the Western reining and braking techniques don't require quite so much arm muscle as riding English can do.
Arguably, a bigger horses trot and canter is a lot more comfortable than a little ponies, and so easier to learn. What's far more important than size is attitude and training. I'd range put my son on a well behaved horse than an evil pony.
All that being said, I am now on the hunt for a pony here, and am looking for a 12hh -12.2 pony. But this is more because that's what he's used to - if someone points me at a perfect 14.2 I'd be happy.