I agree with Trevor on one point.
If we are to believe that we have free agency then yes God would allow a nuclear war. The critical question is 'would we allow nuclear war?'
God's 'job' isn't to stop death and destruction - making up responsibilities for God is something that people who want to blame God for their own failings/feelings of helplessness. Passing responsibility onto anyone but themselves is a real problem in society.
When we kill the last pandas, tigers and elephants it wasn't God who did that, when we wreck the environment with pollution that's not God's doing, when we ignore the majority of instructions in the bible and then whinge about our crappy lives that's not God's doing, when we vote for politicians who are as corrupt as we are that's not God's fault, when we invent nuclear bombs and drop them on each other that isn't God's fault either.
Until we stop looking to the heavens for some divine intervention to sort out our mess we aren't going to solve anything. If we want to graduate from the school of life we have start being responsible for our own lives. If you hate the idea of nuclear war, vote for anti-war representatives, join Greenpeace, do all you can in your community to avoid inflaming nationalistic feelings and hate and then for good measure get yourself an evacuation plan and food storage in case the worst happens and your not at ground zero.
I've seen miracles happen but they always came when people were acting for themselves and doing something about their life. Its far easier for God to steer your course when your moving than when your sat on your pooper.