Only one dog is shown in the movie. It is brief, and the dog is running towards the good guy. Dog is shot at, but main character kills a girl instead…accidentally. It never shows what happened to the dog, but briefly talks about main character being in the stockade because of the girl’s murder.
It doesn’t show any animal being harmed. You can’t hear any either. However, there is a question about whether horses in the corral were hurt during a scene with dynamite. It’s just unclear.
The scene where the main character’s horse was about to be shot works out fine. The horse is not hurt at all.