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 much solar energy Earth receives in a day and say how many zillion times its more than energy of bombs combined, lol.
Note: you just might by dumb luck be factually correct, but your argument is motivated cognition. Nukes are scary, and hence very motivational. Goes both ways.
You are saying, that the total energy amount of all the nuclear weapons is 4*10^18 J. Not 40 times less as I have said.
Even in that case, the wildfire which has covered 5 million square kilometers and consumed 1 kg of dry grass and wood was a bigger event. Especially since I gave 10 times smaller energy per kilogram of wood or dry grass as it is. It's 10^7 J/kg not 10^6 as I have calculated. Not to mention, 1 kg per square meter is a very low number.
But it matters only a little. This calculation is not very exact, but quite enough to see the main point.
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.