All through the nose. Although on long-haul flights I get similar problems as you, Hovis (but without the phlegm thing... eew.
). The air is so harsh and dry I run into all sorts of problems trying to breathe comfortably, no matter which orifice I breathe through...
Pointless fact:
During winter in cold regions (In my case, Canada) you're supposed to breathe through your nose to warm up the air going into your lungs to help keep you warm.