The beginning of winter can be calculated in any number of ways. There is astronomical winter, which begins with the winter solstice on Dec. 21. There is the climatological winter, which begins on Dec. 1 and lasts precisely three months until the last day of February (although that date can vary).
Obviously, in some years, winter weather will have begun well before either of these two dates so they are not all that useful. We could use the first day of snow, but early snows are often followed by mild fall weather. We could use the first day of permanent winter snow cover, but that is problematic because we cannot know which snow that is until long after it has fallen.
Perhaps it makes sense to go with the municipal winter. For my neighborhood, that date is Nov. 15, which is the first date of alternating avenue and street parking restrictions. This seems to work as well as any other.