The Cold War absolutely did not feel resolvable at the time. The popular conception was that of present day North Korea cranked up to 100; there were crazy people in Moscow, they had thousands of nukes pointed at the rest of the world, and they’d successfully set up a system to prevent sanity from being restored. (In Russia, my understanding is that they generally saw it as a story of capitalists who could not stand to let a worker’s movement survive; in the rest of the Warsaw Pact, they saw it as a permanent system where the country must remain communist because the Red Army will invade otherwise.)
* At least in the US, the fear of nuclear annihilation was partially offset by the belief (which was never officially substantiated) that the government would adhere to a policy of rational deterrence, i.e. MAD. It’s hard to find polls on belief in MAD, but friends and family I’ve talked to have stated that it was a source of reassurance during all but the most stressful moments of the Cold War.
* The stress of the Cold War also coincides with the longest period of peace and greatest increase in quality of life in the Western world. An intuitive explanation of why suicides didn’t increase under the stress of the Cold War is that life was otherwise improving for most Westerners in tangible ways. The relative stagnancy of the last 30 years is a significant departure from that.