I would point out that ice caves are actually not a very effective hiding spot. Machines and technology are possible because of entropy - energy flows from concentrated/high-energy states into more dispersed/low-energy states, and in the process you can derive some work - some desired change in your world - from it. However, that change also creates heat, either directly or indirectly (machine interacts with environment, disturbing molecules and heating the environment as it does the desired work, or machine's own molecules are agitated as they process the energy from one state to another, heating the machine). Even if you imagined a perfect insulator, you'd then have a machine that worked only within the insulator: it would be imparting energy - and therefore heat - to the external environment the moment it tried to act on the world outside the insulator.

If you postulate a base entirely enclosed within a perfect insulator, then you've got another problem: the base is heating up as its machines do work, that heat can't leave the base, and it will eventually cook within its own waste heat.

That waste heat thus must be discharged. Short of that perfect insulator, at least some would discharge into the vicinity of the base, slightly heating the surrounding environment. That discharge even if relatively slight would be detected by satellites, especially since we're putting so much effort into learning how the planet handles heat right now and therefore paying greater attention to the icy zones, what with the global warming scare and all. It would be questioned, since it would throw off people's theories about how much heat SHOULD be at that locale. And it would be investigated - scientists being rather defensive about their pet theories and irritated by anomalies that seem to discredit their theories. Any Little Green Man worth his salt would realize that and would therefore avoid any locality where his/her/its base's heat output, however small, would stand out in greater contrast against the surrounding cold environment. Thus, icy places are not a good prospect.

Underwater is good, since you can sink a base deeper in water with a good deal less work than you can in ice (and with no surface evidence that you'd done so), since the temperature of water is higher than ice and therefore yields less contrast, and since the water will flow and carry heat away, dispersing it over a wider area. On the other hand, the recent Cold War prompted some very careful mapping of the sea floor in order to better deal with present and future submarines, and nothing obvious stood out, though if it were small or took pains to camouflage itself, it could have been missed.