I was there in March and it was absolutely freezing but nice and sunny. If you like sightseeing, I'd recommend the Copenhagen card (I think you can use the wifi at the airport with it) but make sure to make the most of it because it's not cheap. Opening hours in March are not great. Some things aren't open at all until April or May (yet you still pay full price for the Copenhagen card)
Insider Tip:The museums are really very good (especially the Thorvald Museum and the Glyptothek) Free wifi in the Library!!