Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
This war movie won four Oscars, including best director for Oliver Stone and Best Picture. There are at least two Best Picture Oscar winners with snakes in them that I know of, Nomadland being the other one, and yes I have watched every movie that ever won the Best Picture Oscar, even the really bad ones, but some of them I watched long before I was snakespotting, so I might have missed some. (There are at least nine movies with snakes in them that were nominated for Best Picture, though I haven't seen all of the nominees.)
The movie stars Charlie Sheen as Chris, a new US Army soldier who just arrive in Vietnam during the war in the late 1960s. The movie is determined not to glorify war, so much so that the US Army refused to help with its production. (The military prefers to promote war films that will help them attract more recruits.) We see lots of the horrors of combat in a tropical jungle in the movie - the worst being that there is an army of armed men out there trying to sneak up on you and kill you. Besides the obvious combat threats of death or injury there are lots of other difficulties - opressive heat, pouring rain, rough terrain and impassible vegetation, and the heavy gear you have to carry. There are also lots of dangerous and annoying creatures in the jungle to worry about, including your fellow soldiers who constantly pester you and might even try to kill you if you cross them, along with venomous ants, mosquitoes, leaches, and, of course, snakes.
During the opening credits we see Chris hiking through the jungle with his platoon. He sees a snake on the ground nearby (a cobra) then lifts his machete to kill it with, but he ends up just walking past the snake. He is either afraid, or he has learned not to react to every possible threat. Shortly after this he is covered with ants and needs to sit down. After other soldiers help him get rid of the ants, he faints.
Later in the movie when Chris is standing guard, he looks down and sees a snake crawling between his legs. We first see his face looking concerned and we don't know why, but think it could be the enemy, but then the camera slowly moves down from his face to show a snake wrapped around one of his boots. It slowly crawls away and Chris' only reaction is a startled face. He doesn't make a sound and doesn't try to kill the snake.
It's unusual to see snakes in a war movie that are not there just to be an adversary to be shot or hacked to death to prove someone's bravery or their violent nature. That's part of the genius of this movie, that we don't always see what we expect to see in a war movie (in 1986.) In most war movies, even today, there would be an immediate bullet or machete to the snake's head. I'd like to think Chris is smart enough to know that there is no reason to kill a snake, especially when firing a gun could give away his platoon's position to the enemy, but this is a movie, and Chris is the main character, and his character development is what we're there to see. Maybe I'm reading too much into this, but I think Stone is using the snakes as more than just background. One snake in the movie could be considered insignificant, but two snakes encountered by the movie's protagonist who does nothing to them has to mean something more. I think we're supposed to think that Chris has not yet learned to confront evil. He is not yet brave or experienced enough, or maybe not yet angry enough, to take action and kill the snakes. But at the end of the film he does finally act on an evil worse than a snake when he kills Sgt. Barnes who killed Vietnamese civilians and Chris's platoon leader. There is no doubt when we see Chris at the end that the war has changed him. He's a better soldier, though I don't know if he's a better person.
Both snakes used in the movie were live animals. It was filmed in the Phillipines, so I assume the snakes were from there, but I don't know what kind they are other than that the first one is a species of Cobra. Since the second snake is actually crawling around the feet of Charlie Sheen, I have to assume it's a completely harmless species.