Miranda Marcantuno is a gymnast. But instead of gymnastics in a gym on bars, beam, floor, or vault she does gymnastics on a horse. So, she doesn't do floor on the horse, bars, or beam vault. Pretty much, it's like ballet on a horse. Miranda's team is called the Vaulting Visions. Miranda is 11 and in 5th grade. Her team is a national champion team. I wouldn't do this because gymnastics on a moving thing just doesn't seem safe.
Gymnastics is a hard sport and dangerous because you can break bones falling off the beam or bars. I saw someone who dislocated her shoulder just by putting her hand in a slightly wrong position when doing a roundoff-back-handspring, a flip-flop. So, no matter where or how you do gymanstics, you must be careful.
You can read more of gymnastics on a horse on The New York Times.