Vehicles slow down and often need a push from the nearest Good Samaritan to get out of a rut. You begin to see people opting for the walk instead because it's safer and less hassle than car-defrosting rituals. They troop out in the middle of the street following the pioneering tire trails of that guy that owns the pickup truck. Everyone seems to slow down and shift their priority from getting there as fast as possible to getting there safely. People become people again, not drivers or sociopaths or whatever mindset we acquire behind the wheel (See Louis CK). You also see people outside just for fun. When I was a kid, snowbanks brought our neighbourhood together like nothing else. My family hasn't grown out of that. Here's Ryan and I having fun after a major snowfall with the GoPro and Spooner Board (to my brothers reading this, I'm bringing this home for you at Christmas - couldn't help testing it out first :P).
Here is my view from the sidewalk on the Monday after a big snow. I should note that by evening, the city had taken care of most of these snow barriers.
Consider that almost everyone is a pedestrian at some point every day. However, there is a large segment of the population that is "too young, too old, too poor, not able, or not interested to drive." (1) As cities, we should prioritize sidewalk clearing so that (among other things) young children don't have to walk to school on the shoulder of the road, concealed from drivers by snowbanks, being showered in the slush spray of passing cars.
Many four season cities prioritize pedestrians by enforcing the responsibility of sidewalk clearing on property owners. Of course, not everyone is capable of shovelling a metric ton of snow. Chicago is getting around this by experimenting with crowdsourcing their snow removal. Their volunteer Snow Corps will soon be able to "Adopt a Sidewalk," counting on generous citizens to ask not what their city can do for them, but what they can do for their city. Boston inspired the idea with their Adopt a Hydrant program, where volunteers commit to shovelling out a fire hydrant. These initiatives suggest that it's possible to clear sidewalks without leaving the roads snowed in and it's also possible to ask more of citizens.
We've seen it before: the little kids shovelling their elderly neighbours' front walk or the family with the snowblower clearing the whole block's sidewalk. Great neighbours make great cities. I'd argue that plenty of casual encounters, maybe while walking about or shovelling snow, make great neighbours. So let the snow bring us together and long live the four season city.
EDIT (Feb. 5, 2014)
Pardon the video overload, but I just found this video by Streetfilms that sums up the sentiment brilliantly in a snowy New York City. Enjoy: