No one goes to work or school for a couple of days. People usually stock up on essentials in the days before the storm. (Milk, bread, butter, eggs... the old joke is that everyone has a sudden urge to eat French Toast.)

Plows usually start early, while the snow is still falling. Plow and salt crews work night and day. They're on call (and paid a stipend) during winter for this exact reason. The main streets are prioritized. Residential streets are going to wait a couple of days before they're clear. With nothing else to do, the adults start digging themselves out and helping their neighbors dig out. It's a hell of a workout and a good reason to check on elderly neighbors.

Basically, you wake up, say "fuck this shit," call in (or not, because your boss isn't at work), and go back to sleep for another few hours. Then you start digging.

A city that doesn't get that much snow can get overwhelmed, though. Mayor Mel famously called in the military to clear snow from Toronto back in 1998-ish. That was only a meter, but the city didn't have the resources to clear it - or more importantly - any free space to put it.

Buffalo though? Buffalo has their snow systems down.