Snow will develop between 7 and 10 AM across the D.C. Metropolitan Area.
Snow will continue, possibly mixed with rain through the early to mid afternoon hours. Snow flurries will end from west to east during the evening rush hour.
Accumulations will be found mainly on grassy surfaces with one to three inches possible.
Here is a look at the latest high-resolution, short-range model (4km NAM):
Here is a look at the latest Snowfall Accumulation Forecasts from the Various Models:
The winds will really pick up on Tuesday night with gusts to 45 mph possible. Wind chills on Wednesday morning will hover in the single digits and teens with actual air temperatures in the lower to middle 20s.
DC Storms 
I agree completely with your forecast. Pretty good consensus of 1-4″, assuming it sticks. Probably won’t on roads.
The one way it could be a significant event would be a heavy burst of instability thundersnow, if the air aloft gets cold enough.