I did the lights cruise on QV last fall in November. There was snow on the ground at our northernmost ports, Tromso and Narvik. Not a lot, but some. As for the lights, we are in a maximum period, so you have a good chance. We saw them on three nights.
You mentioned Viking in January. And advantage to November is that days are longer for doing some sightseeing. Sunset is still early. IIRC, it was around 3 PM in Tromso. But not as early as it will be in early January. Also, it isn't too cold. In the north it was around freezing plus or minus a few degrees. And in the south, it was still autumn. We saw some pretty fall colors in one of the southern ports. So a nice mix of experiences.