You might be able to keep it pretty warm in there, but I think it would be tough to keep the holes thawed. I would think in order to do that, the ice would melt all around.
Keeping the ice thin on them might work if you go a day between trips, but much more than that and you'll have at least some freezing. A hand auger might work then, instead of firing up the gasser everytime.
I haven't had a shack in years, these other guys will be able to answer you better.
