Hi Hacksaw,
In your scenario, the effects of windchill is not a minor issue. A tent will keep you sheltered much more efficiently than a windbreak sil tarp. A good tent will raise the air temperatue inside by anything up to 10-15C, if the air temperatue is say -15C. Using a candle latern such as the UHO candle latern will help even more to raise the inside temperature. The extra weight and bulk of the tent will be just as valuable as a using a sleeping bag.
If you want to keep weight and bulk down you could always use the following system from Alpkit. By using a very lightweight (450gm) half bag in conjuction with a down Jacket you could save on weight and bulk here on the sleeping system then make up the difference by getting a proper tent. Sometimes only a proper tent will do and good ones are very lightweight considering what they can acheive in this survival scenario.
I'll have a space blanket ground sheet to reflect heat back and an air mattress to keep me up off the ice and eliminate heat loss by conduction
On ice the air matress will probably require an addition pad underneath, something like a Thermarest Z-rest. This will dramatically improve the thermal resistance of the air matress for little additional weight but will be much more bulky.