Hands and feet. The feet, for me, are the hardest. I can never really keep them warm unless I'm wearing heated socks. And they don't last a long time.
But hands, if I was touring in January, I'd buy some pogies or moosemitts. I'd probably also have some chemical warmers as backup.
I think for clothes – same as if you were backpacking – layer as appropriate. Some rain pants and jacket without a doubt, good base layers, and a breathable mid layer. I've ridden plenty in the winter, but only 2-4 hour day rides, never toured in winter.
If you're going to be in the DC area at all, let me know and I'll PM you my phone number. If you need a night in a house instead of a tent you can crash here, dry your stuff, take a shower, etc.