Supposed to be a fairly normal winter, so maybe a half dozen snow storms...figure only three of those will really affect the trails, so just call in sick those days and your set!
In all seriousness, take some time to familiarize yourself with the roads and trails before you start commuting to Tyson's...there's little to know bike infrastructure out that way and it's a traffic nightmare. I have no hesitation about riding pretty much anywhere in DC (I live in Capitol Hill), but Tyson's would scare the bejeebus out of me. But I think the best route for you would be W&OD to Gallows road, which has a shoulder/bike lane for at least a portion of the way into Tyson's...but I don't spend much time out there, so others may know better.