This is actually contrary to other research that shows this fear is a learned social behavior in monkeys (read about the studies in Temple Granden's book.) If monkeys encounter a snake in a group of monkeys that haven't seen a snake, there's little reaction. If they've seen the snake and they're in the company of a monkey who's fearful of snakes, then they will all scream and run away the next time they see a snake.

The cultural concept of "fear of snakes" is pretty much a European/Christian based one. There are many cultures where no one is afraid of snakes (they're welcomed as prey animals) and many cultures where they are messengers from the spirit world (the AmerInd cultures) and some cultures where they are worshipped (India.)

And very few snakes live in trees.