One of the scariest things about nukes is the secondary effects. After the cities burn and civilization falls apart. Imagine all the industries that deal with dangerous materials. Imagine what will happen after they are all simultaneously damaged and/or abandoned by the war. You would have tens of thousands of major industrial accidents occurring all at once.

Vats containing chemicals more dangerous than in Bhopal would leak. Nuclear reactors all over the world would melt down with no one to contain them. Oil wells would rust and burst.