"Even if you get to DC, unless the location you arrive at and are heading to are connected by underground Metrorail station (which is the only transportation operating), you'll end up stuck. No Metro buses. No above ground Metrorail stations. Few taxis. Dangerous to try walking more than a couple of blocks."
If you're travelling by air, Saturday should be fine. The snow will stop by Thursday. Just a reminder, next Monday is a national holiday in USA, president's day.