If there are cities under the ice I would be surprised because of how and why the ice forms. As long as the magnetic field lines of the Earth keep their axis and are of sufficient strength the poles will be iced over. Perhaps at a time when the poles shifted there would have been a period where it was mildly habitable there. I doubt long enough for any real civilization to establish itself, though I'm guessing. Perhaps ice cap now covers a plate which moved from somewhere more habitable, again I am guessing.
If I were going to build a modern secret base I would do it under the Antarctic ice, no question. Do all resupply and communication by submarine routinely, no transmissions from the base. It would be great for doing clandestine research, though I do hope the US gov and others don't take their nukes and germ weapons for a walk there given the overt value to the planet the ice caps represent.