I made a proof-of-concept adjustable spade bit tonight. It worked pretty well on ice, although the poor design resulted in the cutting blade rotating around the machine screw. This caused the bit to bore a conical hole rather than a cylindrical hole. Even so, it was an effective proof of concept.
I also tried my jigsaw on ice for the first time. It was terrible. In general, it seems that power tools capable of automatically clearing snow from their cutting blades (chainsaw, circular saw, spade bit) rock while tools that harbor packed snow (twist bit, jigsaw, hole saw) suck.