A world wide nuclear war would drop temperatures worldwide by 20 to 35 degrees Celsius worldwide year around

Note: Of course this presumes the planet stays intact rather than blowing apart in pieces like the Asteroid Belt planet which a piece of killed all the dinosaurs 65 million years ago here on earth. A Soviet Russian Probe sent to the asteroid belt in the 1970s confirmed the asteroid belt had once been a planet destroyed by thermonuclear weapons because of the radioactivity there in the asteroids. It would be interesting if the asteroid that hit earth creating the gulf of Mexico is still radioactive 65 million years later underwater. However, half life's of radioactivity likely ended millions of years ago. However, Fukushima's meltdowns included a reprocessor of nuclear weapons grade plutonium which has a half life of 25,000 years. So, likely it will be 50,000 to 75,000 years before it will be safe for humans to be near Fukushima after that meltdown.

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Whereas a much larger number of firestorms,^[quantify] which are assumed to be the result of any city-targeted, US-Russia total war, is modeled to cause a much deeper nuclear winter, with catastrophic summer cooling by about 20 °C in core agricultural regions of the US, Europe and China, and by as much as 35 °C in Russia^{.
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Nuclear winter - Wikipedia, the free encyclopedia

A drop in Temperature of 20degree C is equal to a 68 degree Fahrenheit drop and a drop of 35C is equal to a 95 degree drop in temperatures Fahrenheit by the way.

So, basically if a world wide nuclear war didn't cause the planet to break apart like the asteroid belt planet did, it would cause an Ice Age likely between 3 to 10 or more years long. My thought is that most people still alive after the nukes hit would die because they only would be able to raise food near the equator. But, even this might be wrong because the sky would be covered with clouds of ash and dust which would likely prevent the sun to be seen at all for years and years.

So, unless you had a power source and grow lamps nothing to eat would grow at all on earth except maybe in the oceans (debatable).

So, generating power so you could grow food might be the difference between human extinction or not.

So, all plants out in the open would die for years including trees, humans would starve and freeze to death unless they had enough technology to stay alive like gasoline and diesel generators (because solar cells would all be gone for years because of no sun). However, wind power likely would still be useful as long as they didn't freeze up in the cold. So, colder weather oil or synthetic oils would have to be used to lubricate wind generators.

However, maybe a few hundred million world wide to a billion might survive worldwide until the sun came out again. So, if people had seeds they could again grow food and survive if they weren't too near high radiation sources then.

So, as long as people didn't mutate too much from nuclear radiation the human race might go on and 10,000 to 25,000 years from then maybe nuke out civilization once again or something like that.

But, this is all theoretical at this point unless one of you is a time traveler and has actually experienced something like this first hand. 

So, basically all plants and animals likely would die including most humans. What would happen in the oceans is more debatable. However, ocean going dinosaurs like Whales and sharks didn't die in a nuclear winter when the asteroid hit earth 65 million years ago. So, whales are the big dinosaurs that didn't die.

So, maybe it is possible for things to go on living in the ocean during a nuclear winter even though most things (except seeds) would die on land and a few creatures who crawled into holes in the ground to keep warm and found ways to stay alive.

Note: Even during a nuclear winter caused by either an asteroid hit of earth or an actual nuclear war that you still could grow food in space and on the moon if you had enough water and equipment. However, I don't think it would be cost productive unless it just was for people in space or on the moon to consume.

However, it is possible that food could be grown in earth orbit in some way if the water problem and soil problem could be solved even during a nuclear winter.

So, food could be slowed down and parachuted down from space orbit theoretically. However, I don't see how right now it would be cost effective to do this. However, where there's a will there often is a way. 

The other thing about this is that if we are in a Geomagnetic Excursion then we are on our way for an ice age right now. Because Geomagnetic Excursions are associated with Ice Ages. 

Also, we either are in a Geomagnetic Excursion or a geomagnetic Reversal right now. However, scientists either aren't sure which or they don't want to panic everyone on earth.

So, what I'm actually saying here is: 1. an ice age may be in our future

and 2. Global Warming is more likely to be caused by the Geomagnetic Reversal or Geomagnetic excursion than Global Warming.

However, we aren't hearing about this because governments don't want to panic the  public, (at least yet). or ever.

But, a Geomagnetic excursion lasts around 1000 years or more whereas a Geomagnetic reversal lasts up to 10,000 years.

And the second one is much more serious for the human race to survive even though either one is pretty serious for humans with an advanced technology culture and even worse if they weren't technologically advanced.

However, it is important to note that an ice age is a completely different thing than a nuclear winter because in an ice age you still have the sun but a lot of cloudy days when it is snowing year around likely down as far as Mexico or further year around. And it would snow down past Italy maybe into the Middle East which might make equator regions of the world like Africa and South America the Bread baskets of the world where the most food would be grown during an ice age.

So, what I envision that is logical to me is Global warming increasing evaporation. Evaporation increases clouds. Increasing clouds means less sunlight reaches the earth. Less sunlight reaching the earth combined with winds decreases surface temperatures on lands. Lower surface temperatures on lands causes snow to stick and grow on lands. This then starts to create it's own colder temperatures sort of like a refrigerator. 

So, for example, the Pacific ocean could be really really hot even up to 90 like now or100 degrees some places in the future (which increases evaporation at the surface). Even under these conditions an ice age could occur with the above scenario and cycles in place on land, especially if the polar vortex drops during a winter down into the Eastern or western U.S. or both areas at once and stays down into the U.S. or Europe or both for very long during this extreme evaporation cycle off the ocean.

So, my premise would be that 90 to 100 degree Fahrenheit water in the Pacific Ocean is compatible with Ice down to as far as Mexico on Land. However, then I have no idea how long this would last (more than one year or two) but I could see this happening for at least one year or more where snow does not melt during the summer because of too many clouds and the snow refrigeration principle of wind blowing over deep snow.

My question would be then: "Does the Pacific ocean keep getting hotter from sunlight or does the land start to cool the Atlantic or Mediterranean Ocean from the wind blowing over the ice and snow on the North American continent or european continent? 

Because the prevailing winds tend to be off the Pacific and towards the east at least as far as the Atlantic Ocean. I'm less sure what winds do from there even though I know there is sort of a clockwise or counter clockwise way they blow that schooners used to use in the 1600s, 1700s and 1800s to get from Europe to either the Caribbean then up to New England and then over to England or the reverse.

Though I'm sorry I got off track of temperatures being brought down by a nuclear war, the more likely scenario we will experience this century or the next I believe is an Ice age. Because the human race has matured a lot in regard to nuclear weapons. The most dangerous time I believe was the first 50 years which we have already survived as a World Culture. 50 years was 1995. We are presently at 70 years since Hiroshima and Nagasaki.

So, we need to move on to figure out now how we are going to survive a potential ice age because of a potential Geomagnetic Excursion during the next 100 years.

The same thing could happen from an Asteroid just like 65 million years ago also.

So, I believe now both scenarios (geomagnetic excursion and an Ice age) are far more probable and likely than a world wide nuclear war for now.