If "complete and total global nuclear exchange" means "we shoot off all the nukes we've got", then how bad that is depends on how many nukes there are - not whether we shoot all of them or not.
"Complete and total global nuclear exchange" is not so bad when there are 50 100Kt nukes, and is really, really bad when there are 10,000 10Mt nukes. And we've drastically reduced both the number of nuclear weapons and their average yield since the cold war (https://fas.org/initiative/status-world-nuclear-forces/). Which is great news!
I'm no expert, but from a little reading it seems all-out nuclear war would be not just survivable for the species, but not even that bad for most of humanity comparing to disasters of yore. South America, Oceania, much of Asia, and Africa would be ~fine.