There is a correlation between the AO phase and the ENSO state, and the AO is the index most highly correlated to snowfall for DC-BWI. The NAO is almost always in the negative phase when there is a negative AO, so the NAO is a factor. I don't have the numbers, but I would bet a predominately -AO for DJF is more likely during a Nino than a Nina. Not sure if there is a large enough sample size, but a Moderate, CP-based Nino might have the highest correlation to a -AO. @psuhoffman can probably give the numbers off the top of his head.