I enjoy tarp camping in winter. I usually go out with the intent of building a snow shelter, but bring a tarp in the event that time is limited or snow conditions are inadequate. I also like to cowboy camp if conditions permit.
A tarp will not keep you as warm as a tent, and spindrift tends to blow farther then rain, making it likely that you will get dusted even under a 10 x 10 tarp. If you zip up the hood of the bivy, the mesh will keep this off your face, but condensation then becomes a slightly bigger problem. These disadvantages can be offset by building snow walls around the tarp.
I second Roger's advice. Try it in a place where you can easily bail out if needed (but not your backyard- that's too easy). I always bring a shovel. I also overcompensate with sleeping gear (-20 bag for the midwest) so there may not be a big weight savings, at least for me. I just enjoy the technique. Also, there is little chance of rain in the dead of winter here. Not sure what conditions are like where you are.