When ones face has been so weathered by smoking, drug use, alcohol, fake tanning or simply acne, that they look much older than they actually are, or that they stuck their head, and only their head, out the window during a hurricane.
One does not need to partake in all above activities to have a hurricane face, but more activities will cause higher degrees of hurricane-appearance.
Similar to, but more extreme than a "leather face".
-Dude, that guy looks pretty old to still be in college.
-No man, he just has a hurricane face, you know, like he stuck his head out the window during Hurricane Katrina.
-I thought she was a leather face last year, but DAMN, all that fake tanning on top of a pack a day has turned her into a hurricane face.