As far as I know, underground water never freezes, but it will be able to freeze if he level it's on has EVER been exposed to the surface. What makes the glacier so difficult is the solid ice is counted as transparent, and thus makes every square down to the rock underneath it vulnerabl.e to freezing.
And I say drunk fortress should be a bonus, but not essential. You get a dragon cookie for running a full turn while at least buzzed. o3o