Well, you'll NEED the ground pad. THat is my biggest worry in what you are trying. Those bags aren't going to do squat on ice/snow if there is no insulation under you. From now until April, I might go out without a bag, but never without a pad rolled up and attached to my pack.

In the lake scenario you are describing, I would say that getting to land or finding other kinds of shelter is critical. You need that wind break in winter, IMO. The other reason why you want to do that is becuase you usually don't find "thin earth" but you can find thin ice easily enough. (Personally, having seen holes in the ice were shanties WERE the day before, past tense, you can't get me to go out ice fishing- nuh uh!)