Depends on the airport, but if it's not open all night, Norway is a bit on the chilly side in winter and I wouldn't want to be hanging around outside for a few hours.

See Trondheim Airport Guide (TRD) - Sleeping in Airports for Trondheim.

I certainly have pulled all nighters - one was at Tromso after a milk run from Kirkenes into an early flight to Oslo. You don't get a lot of sleep