The problem of cold fingers and ears is solvable for more or less any reasonable climate-- certainly for northern Virgina. There are really excellent bike gloves and hats that can be worn under a bike helmet. Having a good pair of socks is also important. Jackets are less of a problem than you would think because they only really have to break the wind-- the act of cycling keeping you warm-- until the temperatures get well below freezing.
The larger problems with winter bike commuting are dangerous road conditions. Ice and slush on the road are bad enough to contend with if you have four wheels, but they can be quite tricky when you have only two. And to further compound the problem is the fact that the bike lanes and side streets that a cyclist prefers tend to be less frequently salted and cleared.