I've sporadically been visiting the Falls Church Farmer's Market on Saturdays. While it's currently less than half it's spring and summer size, there is still lots of local yum to be found. For me, the most exciting has been the pickle purveyor. He must just come in the winter, as he was there last winter (but not spring, summer or fall) too. You can choose between kosher dills, half sours, sours, full sour and something non-cucumber. A few weeks ago I scored some amazing sauerkraut (that I cooked with a local pork roast from Valentine's, roughly following this recipe); this week he had pickled beets. I also noticed someone that had non-fermented cucumber pickles and some other home-canned goods (maybe pickled?) like carrots and green beans. There are still some produce vendors and of course the meat, dairy and baked goods vendors.
There is certainly more gourmet, prepared food to be had as well, even from the produce vendors. And, perhaps because of this, there are many samples to be had. Sausage, soup, pickles, oh my!
Thus, while it probably isn't possible to get all your grocery needs from the farmer's market in the winter, there are plenty of reasons to go.