Watertown is the unfortunate recipient of many of the worst storms that rumble from Canada across Lake Ontario and dump feet of snow on the area. It is not unheard of for a foot of snow to fall on the city in one afternoon during the dead of winter. Add to the general winter weather patterns the problem of lake-effect (water temperature versus land temperature) and prevelant winds from the lake and you get a location which has seen 6-feet of snow in one week.
If you don't have to travel to Watertown during the winter then consider yourself lucky.
If you do have to trave in the area in December through March then remember to have an emergency kit, blankets, matches, flashlight in your trunk. You may need them.