@Celino
There are something like 20,000 nukes extant and if they all went off on target the world population would go down about 90% the first day. There would not be that many folks surviving to worry about nuclear winter.
When chernobyl went off, just that one reactor explosion spread nuclear poison thousands of miles.and that without widespread damage, pretty much confined to the reactor, now melted down and such but it is still nothing like say a one megaton blast.
The survivors would be in a fight for the survival of the entire human race.
I imagine there would be pockets of less ruin that would allow folks to survive maybe in the Andes mountains or some hidden valleys but it would not be a sure bet the folks surviving the 20,000 blasts would just all die later and the latest mass extinction event would set the stage for the next evolution of life on Earth.
The extinctions would extend to the oceans as well as land. Air breathing mammals would probably be the first to die on the oceans since they are forced to surface and breath contaminated air, leading to a slow painful death. Dolphins, whales and the like would be the first to go. Sealions and the like, penquins, all gone.
It would be a total reset of life on Earth just like the half dozen other mass extinctions.
It would take a million years for life on Earth to get back to anything like normal.
Most mammals gone, most intelligent sea life gone, maybe humans gone, if not gone, then reduced to stone age levels, science, gone, math, gone, religion, gone.
They would be relearning how to chip off rocks for tools and weapons.