If your tent has a decent waterproof floor then you shouldn't have a problem with water coming in even if you have to camp on some damp ground. Obviously you don't want to camp at the bottom of a gully or other spot that would have standing water, but I've not really had a problem finding spots that let me camp so the tent stayed dry inside even after (or during) a rainstorm. Furthermore, for winter camping you should have an insulating pad between the tent floor and your sleeping bag so you don't lose too much heat to the ground. So if there is a bit of moisture that comes through the floor it still shouldn't reach your sleeping bag.

If you don't trust the floor of your tent then one approach is to take some thin plastic sheeting (such as used to protect floors while painting), cut it to be just slightly larger than the inside of your tent floor, and put it down inside the tent so it extends slightly up the sides at the edges. This avoids the frequent problem with groundcloths placed under the tent where they end up trapping water between the tent and the groundcloth and forcing it up through the tent floor.

But frankly I'd have to question the wisdom of undertaking a trip knowing that the forecast isn't favorable, you have little winter camping experience, and your sleeping bag is "non adequate."