you da man!

I lived in DC for four years. They don't get much snow, but every tiny bit they get is a nightmare because people drive out of control, they are not prepared to plow it, and sometimes becomes icy in no time. I think that you will be fine, make sure that the car you are driving has all seasons (do not drive with summer tires) and check the weather before you go (extended forecast) so you know what to expect. My father in law has taken the auto-train (do you know what that is?) a number of times and lately he has chosen to drive all the way down to FL.
If there is snow on the ground, and you have the option of NOT driving, take it! Traffic there is bad enough without any weather.