I don't know about water snakes, but a lot of vipers seem to have trouble digesting hair (it's much tougher to digest than bone). But, it doesn't seem to cause a problem. It just passes through along with anything else that's indigestable. I think I remember seeing undigested fish scales being passed by my waters, so I wouldn't worry too much about a little hair.
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What goes up must come down...unless it exceeds escape velocity.