A few inches of snow can ruin the W&OD until it gets warm enough to melt. Freeze / thaw after runners have made tracks turn it into a bumpy ice that is extremely difficult to navigate.
There are road alternatives. Check various side roads, and plan on crossing the beltway on Oak Street, then you can follow Gallows into Tysons. Try to avoid Route 7. And when you ride, you'll smile while your coworkers complain about the traffic.