Nuclear war is usually considered to mean the end of the world. At what point did it become factually true that the USA and USSR had stockpiles big enough that all life on the planet would be wiped out should it come to war? Was it around the hydrogen bomb development in the mid-50s, or later?
This is a hard question to answer for two reasons: 1. lack of clarity on what "unsurvivable" means (some percentage of the world population would survive the immediacy of even the worst nuclear war), and 2. there are technical uncertainties as to the global effect of an all-out nuclear exchange (e.g., whether nuclear winter would occur, whether predicted rises in radioactivity would occur).
In the cases of nuclear winter and global fallout issues, when the raw megatonnage gets to the tens of thousands of megatons range, then it starts to look kind of "unsurvivable" in the sense of "several nations would cease to exist as functioning nations and the world is probably entered into some kind of massive extinction event." By the 1950s the US arsenal reached that point. I do not have comparative data for the Soviet arsenal but theirs started to grow to great size by the 1960s and 1970s.
But you will notice that the US arsenal megatonnage decreased dramatically after the 1950s. This is because lower yield weapons became more favored. The nuclear winter scenario may have still applied through the 1980s, given the sheer number of fires that would be started from a "full nuclear exchange," however. But this is unclear; the modeling is inherently difficult.
It is unclear whether a full nuclear exchange today, when arsenals are actually pretty low compared to what they were (a couple thousand deployed weapons, as opposed to tens of thousands of weapons), would produce such a scenario. They are adequate for destroying the countries (again, not 100% fatalities, but enough to render them "not the nations they were") of the US and Russia, but it is unclear what the global effect would be — it depends on your model, and the models are contentious.
I think people tend to get too hung up on the "100% fatalities" scenario, without realizing how bad even 10% of fatalities ("decimation") would be, much less something remarkably like 30% of fatalities (which is on the order of the percentage of Jews who died in the Holocaust), or something hard to imagine like 50% of fatalities (which is on the order of the people who died at Hiroshima). The Black Plague killed 30-60% of Europe's population, and we still talk about it as the ultimate catastrophe, and the historical, social, and economic effects were profound. Even without killing 100% of people, nuclear war would be a profoundly traumatic event.
