Which cities have the highest chance of snow in Germany? I've heard that Berlin snows every once in a while but on average what are the snowiest places in Germany?
If you can read German, take a look at http://www.winterchronik.de/winter-chronik.jsf#
Depends on you definition of city. In general snow fall tends to be a function of elevation. The place with the most snow is by a large margin the Zugspitze at almost 3000m and it accumulated a whopping 42 meters of snow last winter. It's well developed and fairly easy to get up there (depending on season).
Other heavy snow areas are the Brocken region in the Harz Mountains and Fichtelberg in the Ore Mountains close the Czech border, but these are fairly remote areas.
The town with the highest elevation is Feldberg in the Black Forrest at around 1200m. It is also well developed touristically as a snow resort in winder and hiking in summer.
None of the major cities has much of an elevation, your best shot would probably be Munich at around 500m.
There is a whole spectrum of "elevation vs size" in between the two.
Rule of thumb: The higher, the more snow. You will probably find snow in the mountains in winter (alps, Black Forest, Erzgebirge, ...), but chances decrease as the altitude decreases..
"Source" for this claim: @deviantfan mentioned that Damüls is the place with the most snow in Europe in his comment. Damüls is roughly 50km (beeline) from Friedrichshafen, Germany, where we had no snow at all during the winter 2015/2016 IIRC. Damüls is located at 1400m above sea level, Friedrichshafen at 400m
Unless you define what constitutes a city, it's impossible to give a clear-cut answer.
The snowiest region is probably Allgäu, but its largest town, Kempten, only has a population of 68,000. Balderschwang in Allgäu is Germany's snowiest municipality, but with a population of about 300 also the second least populated.