Max Roser at Our World in Data:
Cities that are attacked by nuclear missiles burn at such an intensity that they create their own wind system, a firestorm: hot air above the burning city ascends and is replaced by air that rushes in from all directions. The storm-force winds fan the flames and create immense heat.
From this firestorm large columns of smoke and soot rise up above the burning cities and travel all the way up to the stratosphere. There it spreads around the planet and blocks the sun’s light. At that great height – far above the clouds – it cannot be rained out, meaning that it will remain there for years, darkening the sky and thereby drying and chilling the planet.