The National Weather Service (NWS) has analyzed the temperature and precipitation for December-January-February (DJF) in years since 1950 with La Niña conditions. They find that there is a statistical correlation between the strength of La Niña and Washington/Baltimore area temperatures: Weak La Niña years have slightly below-average temperatures, while moderate years are slightly above average, and strong years are more above average.
Winter precipitation in La Niña years on average is below normal by about 10%. This is true pretty much independently of the strength of the La Niña. For snowfall, however, weak La Niña years average above the long-term mean, but moderate and strong years have below-average amounts. This is especially true for the main snowfall months of January and February. The NWS concludes that this is the result of the more westerly storm tracks and warmer temperatures which are associated with the stronger La Niñas: "More storms tracking to the west of the Appalachians would imply the mid-Atlantic region being located on the warmer side of storms, resulting in more mixed or rain events for the area and less snow events."
Washington and Baltimore have each had only two double-digit snowstorms in La Niña winters since 1950:
Dates Washington BaltimoreImages (click to enlarge): Washington, DC winter average temperature, precipitation, and snowfall for average, weak, moderate, and strong La Niñas, from National Weather Service, Sterling, VA
6–8 January 1996 17.1" 22.5"
16–17 December 1973 10.2" 7.7"
25 January 2000 9.3" 14.9"
Another winter 2010-11 Washington winter outlook, from Bob Ryan, WJLA-TV (Channel 7):