I have heard that as of yesterday, MVT was ice and snow except at certain bridges where Friends of the Mount Vernon Trail cleared it.
Other trail info – I rode the Four Mile Run Trail on Thursday, it was quite rideable from Shirlington at least to South Meade (IE near the shopping center with the Giant) I have heard that there were issues on the boardwalk by the power facility.
W&OD was rideable from Walter Reed to Bluemont (that was the part I rode today) if a bit narrower in spots. Note most side connections to neighborhoods, like at 7th, or at Park, looked absolutely NOT rideable. Bluement trail was rideable, mostly, though narrower in spots. Lucky Run Trail (by Walter Reed) was rideable, with a couple of spots that were absolutely NOT (solid ice)
Last I heard Holmes Run Trail in Alexandria was still covered with snow.
Around Alexandria and Arlington there are still lots of ramps to crosswalks filled with snow. Bike lanes are iffy. In addition to snow in the bike lanes, cars are often parked well into the door zone bike lanes, as drivers compensate for snow near the curb.