The research commented on and linked to in some threads below don't pass the sniff test. It claims that 50 air-burst Hiroshima-sized nuclear weapons would cause a terrible nuclear winter and a new ice age. Yet neither the 3 weapons at Trinity, Hiroshima, and Nagasaki, nor the 528 air and ground-burst nuclear weapons set off over the next 35 years, most having more explosive power than 50 Hiroshima-sized bombs, had observed effects on the weather. Neither did the many German and Japanese cities that the Allies burned at least as thoroughly via conventional weapons. Much more area burned in Tokyo and Dresden than in Hiroshima.

If they were talking about ground bursts of high-yield weapons, I just might give them some credibility... but 50 15-kt air-bursts?

The Castle Bravo test was a ground-burst test with a yield of 15 Mt, 1000 times the yield of the bomb used on Hiroshima. A ground burst throws much, much more dust into the air than an air burst. I'm not aware that any effect on weather was observed. Perhaps this is explained by there not having been a lot of combustible material at the site of the explosion.

"Heavy fire damage was sustained in a circular area in Hiroshima with a mean radius of about 6000 feet and a maximum radius of about 11000 feet." That's 4 square miles. We have burned an average of 5800 square miles of Amazonian rain forest every year since 1970, again with no observed temperature drop.