Consider the following:
With how many people we have as a species and how frighteningly numerous nuclear bombs are, the likelihood of an accidental nuclear explosion and subsequent nuclear winter is unsettling high. But I think as a species, we'd survive the worst winters, there's just an absurd number of us on the planet, the likelihood at least one community of people survive for the bare minimum of a few generations would be fairly high. People would be born and die knowing nothing but nuclear winter as their reality.
Nuclear winter probably would not happen. At most we would face a nuclear autumn.
1) Every model they had back then used firestorm on every city. There is no solid proof every major cities would burn to create firestorms. I guess some forest fires do as much smoke.
2) Nukes today are smaller and more precise. They would be used as air bursts, which produce less debris. Since the yields are smaller than 15-20 years ago (there are no 10MT bombs anymore), the ashes would not reach the stratosphere. Just compare the mushrooms clouds from 800kt/1mt bombs to 10 mt. Old models used ground bursts.
3) Remember the Kuwait Fires? Sagan (which I do admire) predicted major climate change for the region. Didn't happen, because the atmosphere as a way to protect and regulate itself, with rain & wind.
4) Volcanoes are much more powerful than our tiny bombs. Krakatoa ejecta was approx 19 cube km!!! And the could went 55km high in the atmo. And the effects of this were mild and lasted a year or 2. How many bombs you need to replicate that? Note : Krakatoa was a "small" explosion.
https://en.wikipedia.org/wiki/Supervolcano
There are politics involved in this debate. Freeman Dyson said it correctly, the science of nuclear winter is pretty bad, but how do you defend the idea of nuclear war? You don't.
All in all in could change or end our civilization, maybe, but not humanity, and definitly not life. The Earth and life on it survived much, much worse.