When I was a kid I did vaulting for a few years but I never got good enough to compete. Still, what I remember most is that it was quite shaky a lot of the time, especially when there were more people on the horse and you had to coordinate your movements with them
Yes, those horses are incredible! They have to be able to keep a steady pace while people jump on and off and do their "stunts" out of the field of vision of the horse. They have to be used to that so they don't spook everytime someone comes close from the side and jumps on their back, which is basically what a predator would do in nature. In addition to that, the horses have to be ok with the atmosphere in competitions, foreign surroundings, lots of people, lots of other horses.
I'm not an expert, but as far as I know, if you fall off during a competition (and you are not hurt), you can just jump on again and finish as if nothing happened. The judges will give you zero points for the failed figure, though, I think.
Ok, that makes sense. In gymnastics if you fall you get big deductions and sometimes you don't get credit for the skill (If your feet don't hit first or you don't make it all the way around, etc). Are the horses trained at an early age to not jump? They must be well socialized.
The vaulting horses I know of are normal riding horses and have been under the saddle for some years already. Vaulting is kind of their second job They were chosen by the clubs for vaulting because they had the right size, stature and were quite calm. The horses are regularly ridden, because only running in a circle gets boring and would be one-sided training. Training a young horse might be too dangerous for the vaulters, since young horses often are a bit jumpy and have trouble keeping a steady pace and steady line with a person on the back.