As I've said. All the atom bombs we have, have combined less energy than a big wildfire. So the energy is not a problem.
Then, the amount of "black smoke", which would those bombs emits, compared to a volcano is small. There is nowhere one ton of a black smoke emitting plastics per person alive, not to mention that everything will not be burned.
I don't see where they are getting their numbers. One of those scenarist was Carl Sagan. He made quite a panic when Saddam Hussein ignited those Kuwait oil pumps. He was wrong.
Look it now either from the energy point of view, either from the soot lifting point of view - it is not such a big event in the geological terms at all.
Billion of people may die, maybe more, maybe less. An unspeakable evil, it would be, yes.
But a nuclear winter from an event comparable with no such a big wildfire? One million square kilometers of the Australian bush burnt. One trillion square meters. One kilogram of grass and wood per square meter burnt. One million J of energy released. This is a very conservative calculation, but it gives you 10 times more energy than the combined nuclear stock pile would. And the biggest wild fire covered 5 times more land. So, maybe 50 times more energy released - caused no nuclear winter.
Every year we have enough wildfires to release more energy than there is in those bombs.
You have to put everything in a perspective.
I don't see the total arsenal yield figure, but i have total yield from testing:
http://en.wikipedia.org/wiki/Nuclear_weapon_yield
which is slightly above 500 megatons
For the wildfire:
10^12 m^2 * 10^6 j/m^2 = 10^18 j
1 megaton of TNT = 4 * 10^15 joules. Thousand megatons = 4 10^18 joules. 500 megatons = 2 10^18 joules , 2x your fire already. Multiply by your 10..100 (the arsenal vs testing quoted from yourself), you get 20 .. 200x the wildfire, that's just the yield, not the fires in cities.
And while we are on energy calculating, why not calculate how muc...
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.