I have a perfect example in support of the argument that it's the temperament more than the training...that kid horses are born, not made.
This horse was labeled an outlaw and killer in his younger years after hurting several cowboys pretty badly. When my Dad got him, it was because he had been loaded onto a truck with a load of cattle headed to the slaughter house. His owner just wanted him dead before he killed someone, but my Dad talked them out of it and took the horse for free. It took months, lots of pain inflicted, and sometimes cruel treatment to get this horse rideable for any adult. Even after he figured out that it was in his best interest to listen to the riders, he was still almost uncontrollable. Hot and chargey and arrogant. If he decided he wanted to go back to the barn/trailer, then nothing could stop him. He would climb over fences (no matter how tall), bowl over people, crash gates and pickups and trailers...it didn't matter to him. He felt zero fear of anything. He was 16 hands and 1500 pounds of sheer muscle and F***-you attitude.
Then, one day, this horse was tied to the fence at a roping. My brother was about 4 years old at the time and somehow climbed the fence and ended up on the horse. It was apparent right then that old Buck had found his lot in life. Where, with an adult, he was almost impossible to have a pleasant ride on, for a child, he would do anything and go anywhere. He seemed to know what level of rider was up there and would respond accordingly. Even after I got a bit older and started to ride him, for my brother (who is 4 years older than me) he would blast out of the roping box at full speed with a simple touch...and I couldn't beat
him any faster than a slow trot. If something went wrong with an adult riding him, he would do what he wanted and the health of the rider be ****ed. In the same situation with a child, he would stop dead still and wait until help came; whether the kid was hanging off his side, under his feet, or he was tangled in wire...didn't matter. An adult, he'd step right on you and sneer as he walked away, but a child could be right under his feet and he would fall over sideways before putting any weight on a foot that happened to be on top of something squishy (learned that at a horse show when my brother, who was about 8 at the time, ended up tangled in Buck's front feet)