I was reading through the TV Tropes entry on Nose Nabbing. They have a few entries on grabbing the nose as an offensive maneuver. Of course, noses are good areas to provoke pain and tearing as anyone bopped in the nose knows, but it seems like it would be a slippery surface to try to grab. Striking would probably be easier, but grabbing might give one more of a chance to neutralize an attacker without permanently damaging them.
Under possible practical variations, I have seen self defense drills include the idea of ramming one's fingers up into the nostrils for the combination of immediate pain and control (and probably the amusing mental image of using your opponent's head as a bowling ball), something which again seems to require more precision than one is going to get during a fight.