Or we could just ask everyone to leave their refrigerator doors open

To see what climate effects [a non-superpower scale] regional nuclear conflict might have, scientists from NASA and other institutions modeled a war involving a hundred Hiroshima-level bombs, each packing the equivalent of 15,000 tons of TNT—just 0.03 percent of the world's current nuclear arsenal. (See a National Geographic magazine feature on weapons of mass destruction.)

The researchers predicted the resulting fires would kick up roughly five million metric tons of black carbon into the upper part of the troposphere, the lowest layer of the Earth's atmosphere.

In NASA climate models, this carbon then absorbed solar heat and, like a hot-air balloon, quickly lofted even higher, where the soot would take much longer to clear from the sky.

[...]

Earth is currently in a long-term warming trend. After a regional nuclear war, though, average global temperatures would drop by 2.25 degrees F (1.25 degrees C) for two to three years afterward, the models suggest.

via news.nationalgeographic.com