If it isn't about MJ, then it is about the amount of dust and soot?
Pinatubo ejected about 10 cubic kilometers of dust into high altitudes. The potential energy of this dust was far greater than the energy of all atom bombs. Ignite them all and you will get just enough energy to get 1 cubic kilometer of rocks a few kilometers high.
It was no nuclear winter, again, from Pinatubo.
The atomic bombs are merely the ignition devices - their energy does not go into projecting particles upwards (or very little). The burning cities are the sources of smoke, the close proximity prevents easy dilution of the smoke, and solar heating gets the particles up the last few kilometers before the clouds have time to disperse (incidentally, smoke from forest fires isn't as black, thus the solar heating effect isn't prominent for them).
Just a reminder that some of the old threats are still around (and hence that AI is not only something that can go hideously badly, but also some thing that could help us with the other existential risks as well):
http://blog.practicalethics.ox.ac.uk/2012/03/old-threats-never-die-they-fade-away-from-our-minds-nuclear-winter/
EDIT: as should have been made clear in that post (but wasn't!), the existential risks doesn't come from the full fledged nuclear winter directly, but from the collapse of human society and fragmentation of the species into small, vulnerable subgroups, with no guarantee that they'd survive or ever climb back to a technological society.