As I have never been behind the scenes of a rodeo, I cannot give any facts. I would hope that the animals are well taken care of outside of the event. I can't really imagine that a horse or bull would enjoy bucking around like a maniac...though that's a far cry better than horse-tripping *cringe*
They quite enjoy it and are taken care of well.
Brother, who is a famous bareback horse of JK's, was injured a few years ago (unrelated to bucking) and they had a rather expensive surgery done on him and turned him out for a year until he got well before bringing him back. Most horses needing a plate and screws would have probably been put down or would have suffered while the owner tried to heal it. They just took him in and had it done, kept him up until he wasn't sore, and kicked him out in the pasture to hang out with his buddies while he got well. He came back really strong and kept bucking.
Skoal's Frontier passed away in January of 2012 at 29 years old. He was famous not only for his bucking ability, but because he wore bell boots. His owner noticed that he was bucking well as a young horse because he was knocking himself, so they put bell boots on him and the rest is history. He retired from bucking at 21. Khadafy Skoal was retired at 21 at the same time as Frontier, and he's still living out his days (and was inducted into the Hall of Fame).
A friend of mine raises bucking bulls and actually bucked some of his stock at Cheyenne over the summer. Those bulls are about as pampered as you can imagine. One of his bulls is really cool -- outside of the arena, his 10 year old daughter can pet on him, feed him treats, and even has sat on him. When he goes into the chute and the music is on, he is a different bull. He knows what his job is and he gets in the zone. He gets amped up for it.
When I die, I'm either coming back as a halter horse, a bucking bull, or a rich old woman's lap dog, because those ones seem to have the life.