What is the route you are planning?

Bear in mind stealth camping gets a lot harder when there are no leaves on trees! You may want to reconsider that. Add in the general openness of Delaware and eastern Maryland (which is where I presume you'll be touring) and it gets even harder.

Not to talk you out of camping, but you might try it in stages. First do a winter tour with indoor lodging, then if that goes well, do the next one camping. Off-season motels shouldn't be too expensive, especially along the coast (assuming they are open).
Obviously, it all depends on the weather. I've biked in Delaware on several New Year's Days over the years and it's been surprisingly warm. Or not :-)

For winter camping, I like to take two foam pads. One closed-cell that goes closest to the ground, and then a Thermarest on top of that. It's bulky to carry, though. To deal with the water freezing at night issue, I usually pour a bottle's worth into my cooking pot. That way, even it freezes, you can thaw it by just putting the pot on the stove for a while. And, as suggested, a bottle in the sleeping bag overnight works, too. I also have several foam "bottle parkas" sized for a 1L Nalgene. They do a pretty good job of keeping bottles from freezing. Also nice in that they keep hot water hot for a good bit of time. Make your tea of coffee in the morning and put it in one of those and you are good for a few hours. See http://www.outdoorresearch.com/en/wa...e-parka-1.html