Yes, there is tourism during winter in Ilulissat, but very little compared to summer, when hundreds of tourists flock to the magnificent icefjord, an UNESCO world heritage site. And no doubt about it, this place deserves to be visited in whatever season! Watching the gigantic icebergs spilling into the Disko Bay is a very special and rewarding experience!
During winter Ilulissat is a much more sleepy town and tries to lure tourists with northern lights, dog sledding and other attractions. You can book easily into guided tours into the hinterland, even overnight trips. Dog sleds, snow scooter rides, snowshoeing and boat trips can be booked as well!
I did not make to many plans as I expected to book these things on short notice depending on weather and my mood. It was a wise decision.
I booked the Air Greenland flight from Copenhagen to Kangerlussuaq and a connecting flight to Ilulissat a couple of hours later. As I wanted to be in Uummannaq for a qualifier for the national dog sled races the day after I could stay just one night in Ilulissat. But my flight further north was the next day during afternoon, which should give me nearly 8 hours daylight and a night for northern lights. On the way back I would stay much longer in Ilulissat, to see the town and the iceford.