I can't speak for Russians, but let me share my own experience dating to late 60s/70s/80s in Czechoslovakia.Anyway I was wondering if Soviet or more specifically Russian culture from the 50s/60s had similar issues dealing with the new reality or did the closed nature of Soviet society make it easier for the government to keep those fears at bay?
The official propaganda (directed from Moscow) tried hard to create a feeling of imminent danger of nuclear war. But we have developed ability to perceive clearly not WHAT they said, but WHY they did so. Obviously, the bolsheviks were trying to persuade us that we need communism and 'friendship' with the USSR, otherwise we'd get steamrolled and subjugated by American imperialists.
As for my generation, I can say that we remained quite intact and resilient to the propaganda, and among ourselves, secretly and in privacy only, we agreed that we wished nothing more but to get 'occupied' by those evil imperialists, and the desperately hated Russians would be kicked back to their own, well-deserved wasteland.
So, those were our sentiments in Czechoslovakia. Incidentally, I happened to live in a city with huge Russian garrison, and the encounters with Russians were often absurd, ocassionally tragic, many times funny, but never friendly ones. All in all, together with compulsory lectures of Russian language and literature at school, it helped in developing very good understanding of who Russians truly are.