I'm not arguing whatsoever against action on climate change, I'm just articulating actually how bad a nuclear exchange would be. It's far, far, far worse than most people imagine because they (understandably) couldn't fathom how monstrous the actual war plans were (and are, as far as anyone knows).
Daniel Ellsberg, the top nuclear war planner at RAND during the Cold War, claims that the Joint Chiefs gave an estimate to Kennedy in 1961 that they'd expect 600,000,000 deaths from the US's war plan alone.
That's 600 million people:
1. At 1960s levels of urban populations (especially in China, things have changed quite a lot -- and yes the plan was to attack China... every moderately large city in China, in fact!)
2. Using 1960s nuclear weapons
3. Not including deaths from the Russian response (and now Chinese), at the time estimated to be 50 - 90 million Americans
That's not extinction, that's not even close. Maybe, just maybe, it'd be the end of both western and eastern civilization, but it's nowhere near wiping out all life on Earth.
climate change will happen, and it will do that, left unchecked