When global warming becomes too extreme, some nations especially hit like India and Pakistan might start a nuclear war just to create a nuclear winter to cool things down a little.
https://en.wikipedia.org/wiki/Nuclear_winter
No, they won't do it to get nuclear winter. But of course, they still might do an exchange when ultimately threatened about water, during unprecedentally bad food crysis, as a result of political extremism, etc.
Why? Because nuclear winter is not a solution for their climate problems. If they are smart enough to know how to handle and use nuclear weaponry - mind you it's dramatically more complex than conventional weaponry, - then they are also smart enough to know about ozone depletion (mentioned in very wiki article you link to). This alone will cause more damage to them than any good they could get outta temporary temperature reductions allowed by nuclear winter - ozone layer is extremely slow to regenerate, iirc. Fancy having your face's skin peeling off whenever you spend half an hour in the sun? I don't think so. Nor do they.
But even more importantly, they also know about the fact that prolonged nuclear winter (read link #55 in that wiki article for some details; it'll last ~10 years substantially, give or take a few) - will inevitably, massively and quickly change global air and water currents. Nobody can predict with certainty whether those changes will lead to more or less precipitation over any specific country. Ok, there is some PDSI research done by teams like Augio Dai's team, but those are assuming relatively gradual change - required condition to even try to calculate what the future of global precipitation and evaporation patterns will be.
So, yes, you can lower temperature for several years by means of nuclear winter, but you never know whether causing nuclear winter could cause dramatic reduction of precipitation (much like multi-year droughts we see in certain parts of Africa nowadays), or dramatic increase of precipitation (which we repeatedly see in certain parts of India lately) - on your own country's territory, and also for your "neighbours" (which may end up being very important for you if they end up screwed up and millions of refugees press through your borders, for example - Europe experiences this already 1st-hand). Those effects can easily cause much more harm to any country's agriculture than any good there could be outta reduction of temperatures.
Why? Because water is the key, you see. There are places on Earth where it's extremely very hot but still those places are overabundant with plant growth - Amazon rainforest is your most typical example of this, but basically any jungle anywhere on the planet is the same deal. Increasing temperatures is not what kills life and makes lush areas to become deserts. Lack of liquid water - is. Example, there are temperatures in excess of 50°C in India regularly, but you can still farm in India whereever you got good supply of water - you just need right plants and methods.
There is however a link, of course, between the two: when you increase temperature without increasing amount of precipitation, you get faster evaporation of water, which leads to reduction of water available in soil. Direct effect may be relatively small, but it leads to a bit less plant life, which in turn leads to higher wind erosion, faster seeping of water into underground places (thus leaving top soil drier), etc etc - the thing often snowballs. This is how usually people link hot times to desertification - they just see "it's much hotter and places turn into desert", and start to think it's just that simple - without considering water and actually happening changes in plant, insect and animal life, which all influence the process of desertification quite much. Typical oversight.
As for sudden massive increase of precipitation, - this causes massive harm if happens fast enough (talking years to decades here), because ecosystems and species need hundreds to tenths of thousands years to adapt in this regard. So after that long while, things will slowly improve and in the end, any area getting much more precipitation will end up much more lush than it was before, but until that happens, the area will lose much of its bio-capacity.
P.S. One should also understand that no amount of climate change will ever drive temperatures anywhere close to the boiling point of water, anywhere on Earth. Learning a little physics allows to realize that energy transfer from a hotter body to a colder body is proportional to 4th power of temperature's difference between the two. This is why Earth will radiate massively higher amounts of energy back into cold of near-Earth space even if it's warmed by just a few degrees Celcius, thus preventing itself from heating any much more. Detailed calculations assume that in the end, we may be in danger of having average global temperature raised by some 10 to 15 degrees C, depends on how bad things go (and mind you, +6C is already universally regarded as the end of modern global civilization). But at least the Earth won't turn into anything like the hell of Venus' athmosphere / surface conditions.
I'd actually like to see a winter setting in a Fallout game. It's as much part of retro-nuclear imagery as the desert.
