I'm NYC based, and ran a school in Queens. As a student, from K all the way through 12, school was only closed twice for inclement weather: Hurricane Gloria in 1986 and the Blizzard of 1996. We got hit locally very badly by the 93 Noreaster, but schools were still open that day. None of us from my area made it in.
The snow that we got once I became a teacher and then principal was on a completely different level than anything I saw growing up. But NYC schools are under mayoral control, and who the mayor is made a big impact on whether or not we got a snow day. DeBlasio was quick to close, while Bloomberg avoided it at all costs. DeBlasio being a Brooklyn guy and Bloomberg a Manhattan guy might have a lot to do with that. It's hard for Manhattan folks to imagine how hard it is to get around the other four boroughs during and after a bad snowstorm!