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 "-0.01" temp + precip correlation to NAO(-) in DCA.
I think it's tricky because in the NE, the average temperature dips down to the 40's and upper 30s, which is slightly above borderline-freezing. So a little cold air may be seen to be valued more than it actually is.
Second the PNA, here is temperature and precipitation correlations in the US Winter:
https://ibb.co/6RfXMMT
https://ibb.co/r3BGBnX
There is actually a negative correlation here!
NYC: 0.05 air temp correlation
0.30 precip correlation
so really, a Net "-0.25" air temp + precip correlation to PNA(+) in NYC
DCA: 0.20 air temp correlation
0.38 precip correlation
so a Net "-0.18" temp precip correlation to PNA(+) in DCA.
Again, because it's a cold pattern, and temps on average don't go below the upper 30s/40s, it may seem like those few degrees to freezing are a bigger deal than they are but the conditions are much drier.
Third, the EPO, here is temperature and precipitation correlations in the US Winter:
https://ibb.co/8BJ9Hjk
https://ibb.co/k358zck
EPO has the most +correlation to snowfall, or favorable phase -EPO net resulting in +snowfall
NYC: 0.38 air temp correlation
0.12 precip correlation
so a Net "+0.26" air temp + precip correlation to EPO(-) in NYC
DCA: 0.39 air temp correlation
0.08 precip correlation
so a Net "+0.31" temp precip correlation to EPO(-) in DCA
Out of the PNA, NAO, and EPO, the EPO is the only index that has +raw correlation to snowfall (air temp + precip raw).
[AO is similar to the NAO:
0.5 temp correlation in DCA
0.42 temp correlation in NYC
0.52 precip correlation in DCA
0.42 precip correlation in NYC
so a "-0.02" Net precip + temp in DCA to -AO
a "Net 0" precip + temp in NYC to -AO
Net colder patterns are thought to be more snow-favorable because of where we stand with that 32 degree freezing line.