Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
This is a western starring Willie Nelson as Barbarosa, a notorious outlaw, and Gary Busey as Karl, an inexperienced farm boy fugitive who partners up with him in Texas. This is one of the few westerns set in Texas that was actually filmed there, and there are some beautiful shots of Big Bend scenery.
The snake scene happens when the two outlaws are running from a man who is hunting Barbarosa to kill him to revenge his family. The two climb up a steep rocky cliff above a river. Eventually, Barbarosa, who is wounded, struggles and asks for help, telling Karl to get rid of the saddlebags he's carrying, which are full of stolen gold. Karl throws the bag off the cliff then helps Barbarosa get to the top. Barbarosa then chews out Karl for throwing the gold down the cliff instead of someplace closer. "I didn't say get rid of it down there! We already been down there!"
Karl decides to climb back down the cliff to retrieve the gold. He climbs down to a spot where a rattlesnake is lying inside a small cave. He almost steps on the snake before he sees it. The camera shows Karl from inside the cave as he is surprised by the rattlesnake. The snake strikes at him, but somehow he is able to grab it before it bites him. He must have superhuman reflexes. But the momentum from catching the snake as it jumps out of the cave knocks Karl off the cliff, and he falls down into the river. When we see him come up out of the water he is still holding the snake. Nobody in their right mind would hold on to a rattlesnake as they fall off a cliff, but we already know that Karl is not too bright. He swings his arm and throws the snake away. We see it land on its back on a rock. It looks dead at first, but we see it gradually roll over onto its belly unharmed.
The rattlesnakes used to portray the snake are Western Diamond-backed Rattlesnakes, which in my experience is the rattlesnake species most often seen in the Big Bend. The snake we see Karl catching and holding is obviously a fake snake. It's much too thin to be the same rattlesnake.