Welcome to DC (or technically, NoVA!). A few area sites where you can get local info on the commute:
Washington Area Bike Forum: http://bikearlingtonforum.com/forum.php
WABA: http://www.waba.org/
FABB: http://www.fabb-bikes.org/index.html
BikeWashingtonDC Yahoo Group: http://groups.yahoo.com/group/BikeWashingtonDC

There are some low traffic blogs, facebook sites, and I think a twitter feed for W&OD conditions.

Metro does not allow bikes during rush hour. Folders are OK at all times and all the local bus routes have bike racks so you could take a bus. W&OD is not plowed but FABB reported the Parks authority bought a plow so maybe... Last winter, they did run a plow down the trail to scrape it down to where the sun would melt the rest. Although many sections are well-shaded and take forever to clear. Also, the road crossings will be blocked by snow walls from road plows. Many many drivers are clueless about winter driving, so you'll see a lot of school and government closings. Last winter was rough, but we've had winters where I never needed to shovel my walk.

My commute last winter was shorter and able to use local side streets that were usually plowed, studded tires took care of the rest. One storm in particular - I made it home in just a few minutes more than normal. Icy roads kept coworkers on the road for hours. I have a longer route/destination that doesn't use much if any of the W&OD now, so I may not be as determined a snow rider as I was last winter.

Oh - Capitol Weather Gang (a blog at washingtonpost.com) is a great site for decent weather info & discussions. Good luck!