I don't accept the idea that the climate effect of the fire is in any way comparable to nukes
But you admit, that the energy stored in the nuclear arsenal is hardly as big as the energy released by a really big forest fire?
I don't have a good estimate of energy stored in the nuclear aresnal, and I care about this assertion just about as much as I care about comparison between energy of nuclear arsenal and energy of sunlight that hits the earth in a day.
But yes, I would say it is somewhere within similar order of magnitude, for the yield vs forest fire, ignoring the combustion of items in the cities.
BTW, nukes are incendiary weapons, there's not enough appreciation of this basic fact by public. Don't imagine your house being blown away, imagine all interior catching on fire first, then being blown off. Ditto for all asphalt.
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.