You might be surprised that some of the cold patterns are not big differences in snowfall overall because of less precip.
First the NAO, here is temperature and precipitation correlations in the US Winter:
https://ibb.co/0ZTGpM4
https://ibb.co/sFrQvTf
NYC: 0.45 air temp correlation
0.45 precipitation correlation
so really, a Net "0" air temp + precip correlation to NAO(-) in NYC.
DCA: 0.47 air temp correlation
0.48 precipitation correlation
so a Net