Not exactly.
The second one is just a natural way of saying what happened. He was walking along, minding his own business, and suddenly he screamed when he saw a snake.
The first one sounds more like an answer to a question.
When did he scream? He screamed as soon as he saw a snake. (And in that case, it sound like your listener should already be aware of the fact that there was a snake, so you'd say "the snake.")
What did he do when he first saw the snake? He screamed as soon as he saw the snake, and then got a stick to encourage it to get off the path.
Perhaps there's just something in the first one that makes it sound like your listener should already know about the snake, so saying "a snake" as though there just happened to be one snake of many wandering around doesn't sound right to me.