Unfortunately, I don't think human civilization would ever recover. If we're talking height of the Cold War numbers of warheads, then we're looking at an extinction event that would probably top the dino-killer. If we're talking about today, then most first world places would be still be annihilated, and while humans would likely survive, the utter demolition of society would cripple the world massively. Not a nice life at all.
Then again, I'm not an expert on these kinds of things.
The world would survive, there's plenty of research on this (much of it precisely in order to determine how a gvt would need to react, and such. There's several "theoretical simulations" of a nuclear strike on American targets, for example)
Consensus seems to be that major cities will be wiped out, along with large chunks of their population. Killing
everybody is almost never possible, people- organisms - are notoriously hard to clear away.
So, the initial bombardment would - in worst case scenario - clear out a big chunk (although not all) of the world's urban populations.
Countrysides are vast, and make cities appear only like insignificant dots on the landscape. Countrysides are litterally unbombable. I mean, sure, you can bomb forests and fields, but wtf... ? Look at conventional bombing of hills and mountains, how many Talibans are left to kill? 10 000? Good luck bombing them hills!
People there will deal with the usual fallouty stuff - floods of refugees, rampant sickness (both from the radiation, but also from the collapse of infrastructure, meaning a lot would be infectious), hunger, and the chaos of lawlessness.
People will then not sit around and stare at the wall, they'll get right to work, people need to defend their own, feed their own, look after etc, so that's most likely what will be happening.
A blanketing "nuclear winter" is a matter of debate, so, none of us are experts, so I'm not gonna speculate about it.
So, that aside, there's no real reason that the world's green areas will suffer, if anything, they'll rejoyce, now that humanity has been devastated, production (and therefore harvest, logging, etc) grinds to a halt.
This could be good news for nature
A
very loose estimate for human loss of life during an all out nuclear holocaust, I've seen one place half a billion initially, during the bombardment (worlds urban populations), for then a larger chunk to die off because of the diseases and other long-term effects.
In the end, world population would probably not even be halved.
It would probably disrupt a lot of the global political structure. If there was a UN, this would be difficult to maintain, w all the worlds capitals laying in ruin. Same goes for big, complex federations, like Russia, China, USA, India, Brazil, I have a difficult time seeing these giants keeping together, politically, after their capitals and metropolises have been utterly destroyed.
Organizations like "NCR" are therefore not too unlikely, as local populations would try to secure their own homes - by creating buffer zones, and then borders, and finally governments and armies of their own.
That's tons of speculation tho
Bottom line is - everything is relative
WW2 was the worst war in the history of all humanity, yet it did not even dent population growth on earth - it even
spurred technological research.
Nuclear war will be
yet worse, but still far from the end of humanity, even further from the end of the world.