Efficiency will suffer, as compared to warm weather, but I bet it will be more efficient than other alcohol stoves at those temps. The trick will be getting the fuel to light. Keep your fuel and stove warm until you're ready to light it, and have a lighter (or a lit stick) that will allow you to hold the flame above the alcohl for longer than usual since there won't be many vapors coming off the liquid at those temperatures.
I used another alcohol stove at 2F, and it took 3 matches to get it going, even being careful to keep things warm. When I accidently dunked the lit match into the liquid alcohol while trying to light it, the match actually went out. Once it was going, it worked OK for an overnighter.