Post-nasal drip

I understand this term. It is entirely logical. After all, one could hardly expect one's nose to drip before one had a nose, right? Therefore any dripping from the nose must be post-nasal, that is, after one has a nose. It is the opposite term that puzzles me. If there is a post-nasal drip, logically there must also be pre-nasal drip; and it is hard for me to understand how one's nose can drip before one has a nose.