I don't know about sub-zero, but I can tell you my home-made alcohol stove works fine at 15*F.

I made a Super-Cat stove this fall and tested recently in my backyard. I put 14oz of water in my stainless steel bottle cup (enough to rehydrate a small freeze-dried meal packet plus make a cup of coffee, tea or broth). I then dug a hole in the snow and mounded the circumference to act as a wind screen. The stove went in the hole and I added 1 measured ounce of Everclear (food-grade 90% grain alcohol), then dripped some around the rim of the stove to help heat the can.

I lit it with sparks from a firesteel. I held the cup over the stove for about 30 seconds until the stove and alcohol heated up, then sat the cup directly on top of the stove. I did not use a lid.

Results:

In 4 minutes the water was steaming and developing bubbles, hot enough to make tea, coffee or soup.
In 5.5 minutes I had a rapid boil.
The stove continued to burn until just after the 7 minute mark.

The water came from my BOB in the truck. It was cold enough that ice was starting to form in the bottle. The stove and alcohol were at ambient outdoor temperature.

While this might not be indicative of how it will perform below 0*F, my research indicates good probability that it will work. Adding a reflective wind shield and a lid, or switching to a Ti cup with lid, would improve performance. Carrying the stove and fuel in your pocket would also help.

If it gets down near or below 0 I'll try it again. I also want to see if I can start with snow and wind up with boiling water at that temperature. I'll try to post my results.