Nuclear war (especially during the cold war, when we had much more warheads than now) would absolutely be a big deal and a horrible mass death, but it would not have ended humanity.
Like, if there's a scale of catastrophic events that goes from 0 to 10 where 0 is no big deal and 10 is human extinction, then the worst events humanity has ever seen are somewhere below 1 on that scale and absolutely horrific mass death is something like 2/10 - because the gap between the damage required for that and damage required for extinction is so much larger than the gap between no big deal and worse mass death than we have ever seen. Arguably the worst damage that life on Earth has seen is the dinosaur-ending asteroid, and IMHO a fraction homo sapiens (though perhaps not our civilization) could survive even that. A full scale USSR-USA exchange in 1960s might perhaps kill most people in the northern hemisphere and perhaps cause a nuclear winter decreasing crop yields with an associated famine - but if just a fraction of people in South Asia and Africa and South America survive the famine while the North nukes themselves to radioactive glasslands, that's very, very far from extinction.
Killing half of humanity would literally be an unprecedented level of horror, but it would not end our civilization; killing 90% of humanity would likely end our civilization-as-we-know it but would not end our species, that would bring us to the population level that Earth had in 1700s; and killing 99.99% of humanity would definitely destroy our civilization but it would "just" push back our population growth to the numbers we had ~70 000 years ago - horrific for every individual, but still not an extinction event.
And, in particular, I also think that nuclear winter is another one of these over-hyped scenarios. If you do the napkin-math it doesn't really work out.
Nuclear war will probably result in every major metropolitan area in the participating countries being obliterated. But I'm willing to bet that non participating countries will survive with their civilization intact. Especially countries with high food security that can deal with total collapse of international trade.
Like, if there's a scale of catastrophic events that goes from 0 to 10 where 0 is no big deal and 10 is human extinction, then the worst events humanity has ever seen are somewhere below 1 on that scale and absolutely horrific mass death is something like 2/10 - because the gap between the damage required for that and damage required for extinction is so much larger than the gap between no big deal and worse mass death than we have ever seen. Arguably the worst damage that life on Earth has seen is the dinosaur-ending asteroid, and IMHO a fraction homo sapiens (though perhaps not our civilization) could survive even that. A full scale USSR-USA exchange in 1960s might perhaps kill most people in the northern hemisphere and perhaps cause a nuclear winter decreasing crop yields with an associated famine - but if just a fraction of people in South Asia and Africa and South America survive the famine while the North nukes themselves to radioactive glasslands, that's very, very far from extinction.
Killing half of humanity would literally be an unprecedented level of horror, but it would not end our civilization; killing 90% of humanity would likely end our civilization-as-we-know it but would not end our species, that would bring us to the population level that Earth had in 1700s; and killing 99.99% of humanity would definitely destroy our civilization but it would "just" push back our population growth to the numbers we had ~70 000 years ago - horrific for every individual, but still not an extinction event.