People that lived during the Cold War, what was it like?

I think that one's age and the period of time (e.g. 1988, right before the end, and 1962, during the Cuban Missile Crisis were not the same) would be a factor here.

Nuclear war wasn't a constant topic of discussion in my American experience, but more prominent than after the end of the Cold War.

Russia never lost the ability to conduct a large-scale nuclear strike, so in the sense that Moscow or Washington could trigger a large-scale nuclear war, things haven't really functionally changed.

For most of the Cold War, mutually-assured-destruction was a factor, so I think that few expected an intentional surprise attack.

In some ways, risks were lower. The concern shifted towards nuclear terrorism, which is harder to deter.

And nuclear proliferation has meant that instead of two big camps with mutually-assured destruction, geographical separation and the resources to ensure a second strike capability, you have a lot of parties running around who may have a stronger incentive to perform a first strike. Maybe India and Pakistan -- who have fought directly while both had nuclear weapons, for example:

https://en.wikipedia.org/wiki/Kargil_War

Since Pakistan and India each had weapons of mass destruction, many in the international community were concerned that if the Kargil conflict intensified, it could lead to nuclear war. Both countries had tested their nuclear capability in 1998 (India conducted its first test in 1974 while it was Pakistan's first-ever nuclear test). Many political pundits believed the tests to be an indication of the escalating stakes in the scenario in South Asia. When the Kargil conflict started just a year after the nuclear tests, many nations desired to end it before it intensified.