With regard to the AO and Nina winters, there have been 41 -AO winters since 1950-51. Among those 41, 11 occurred during La Nina years, 14 occurred during El Nino, and 16 in ENSO-neutral. By percentage, this comes out to, 52.3% of La Nina years (11/21), 53.8% of El Nino years (14/26), and 69.5% (16/23) ENSO-neutral winters.
Among those 21 La Nina years at DCA, the average snowfall is 12.0", below the 1981-2010 average of 15.4". In +AO years, the average is just 8.8" with only one season (1971-1972) finishing above average (1999-2000 was exactly average). In -AO Nina years, the average is 14.4", however only 3 out of 11 featured above average snowfall. If you remove the massive outlier of 1995-96, the average falls to just 11.2".
For BWI, those numbers don't get much better. In fact, they arguably paint a bleaker picture. Among those 21 La Nina years at BWI, the average snowfall is 16.0", below the 1981-2010 average of 20.1". In +AO years, the average is just 12.1" with only one season (1999-2000) finishing above average. In -AO Nina years, the average is 18.9", however only 1 out of 11 featured above average snowfall and it's, you guessed it, 1995-96. If you remove the massive outlier of 1995-96, the average falls to just 14.5".
If you break it down by month, in Nina winters at DCA, 4/21 Decembers have seen above average snowfall (3/4 in -AO years), 7/21 Januarys (4/7 in -AO years), and 4/21 Februarys (2/4 in -AO years). At BWI, it's 7/21 Decembers (5/7 in -AO years), 8/21 Januarys (5/8 in -AO years), and 5/21 Februarys (4/5 in -AO years).
Long story short, historically speaking, La Ninas are no bueno for the Mid-Atlantic, which should not come as a surprise. Clearly Atlantic blocking helps, as PSU outlined, but still an uphill battle from there. I'd be interested to see how the Pacific numbers shake up too - I imagine the +AO years had at least a semblance of +PNA/-EPO/-WPO.