Howdy,
The revolver wasn't used much for hunting.
Plinking, entertainment, self-defense and protection were all likely use for a regular cowhand. Of course lawmen, gamblers, gunfighters and outlaws had a different need for the handgun.
For the hand, the revolver was used to kill varmints (or scare them off) to cull a down animal or worst case, to put down a horse, with a runaway as the worst case scenario. He might need it in a fight with rustlers, but again, pretty rare.
Townfolks were more likely to have and need a pistol.
I'm sure you'll get more answers.. Adios,