A cave is a grave.
That was an issue for me too.
One major blast above and you’ll be digging your hardware out for months.
The assumption is that we would deploy before the shooting starts, during a long period of escalating tensions. That’s not necessarily a sure bet, but unless the Russians started a major war as a total surprise (possible but unlikely) or a U.S. administration was frozen in imbecile mode in the weeks leading up to the onset (all too likely, nowadays), there would probably be warning time.
When I was OpsO for MWSS-271 prepping for our portion of an annual exercise in Norway I toured some of the caves. Nothing short of a direct nuke strike would affect the entrance, of which there are multitudes, most of which are quite well hidden.
As to the Nords storing stuff there, in just one of the caves I toured, the US, Britain, Germany and France all had at least one division's worth of equipment stored. Many of the odometers had less than 50 miles on them. I saw quad-cons stacked 5 high that were filled with medical, food, ammunition, POLs and other SL-3 gear. They were all rotated on a 5/10 year schedule to keep them viable.
The amount of equipment there was staggering.