Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
Clint Eastwood, the movie's director, is Bronco Billy, a former New Jersey shoe salesman and ex-convict who re-invented himself as as Bronco Billy, the fastest gun in the west, with his own Wild West show. He's a benevolent dictator to the other performers whom he rescued from their failed lives and gave them a new start in his show.
To open the show, Chief Big Eagle, "the great great grandson of Geronimo", does a "rattlesnake dance." He jumps into the tent in a blast of smoke holding a snake in each hand. He dances back and forth then holds one of the snakes up to his face. The camera cuts away to shocked faces as we hear him scream. We are told later that he was bitten by a rattlesnake, again, and given some of the Doc's snake bite remedy, which seems to be just strong alcohol. We see the Chief later with only a bandage on his lip. When Lefty asks why the Chief doesn't use the gopher snakes that Billy bought for him, Billy says the Chief refused because he's a proud Indian. This is all very ironic since the Chief actually does use gopher snakes in the dance, but the movie switches to a rattlesnake for the close-ups. Billy wants the Chief to fool the show's audience with harmless snakes because they won't know the difference, just as Eastwood fools the movie's audience with gopher snakes, but then Eastwood changes to the correct snake when we see it close enough to know we're being fooled. Most other directors would just continue to use the gopher snakes pretending that they are rattlesnakes, but Eastwood seems to respect his audience enough to make the switch and he even tells us that the Chief is supposed to be fooling us with harmless snakes. This seems to fit in with the themes of artifice and re-invention and imposters who are really more authentic than what they imitate that we see throughout the movie.
The snakes used on screen are gopher snakes, along with a pale rattlesnake that appears to be a Red-diamond Rattlesnake.