Since Tromso is a coastal city, you will seldom see pileups of snow, and as you say, it is rather mild when it comes to snowfall.
I found this page with a chart of average snowfall over the past 30 years (1981-2011).
http://www.tromso.kommune.no/snoe.4547033.html
All text is in Norwegian, but I am sure you could run it through Google Translate if you want a general understanding.
Otherwise, the Norwegian Metereological Institute has a good webpage in English,
www.yr.no, with in depth weather information.
Hope this helps!