I think people overestimate the effects of a large-scale nuclear exchange.
Make humanity extinct? Slag continents? Unlikely. Humans really are like cockroaches, they're difficult to kill.
Also, nuclear weapons are not and have never been implemented as a means to commit omnicide (as much as it may resemble their use). A strategic nuclear exchange would occur between two targets; areas that are not these targets would remain relatively unscathed. As much as people forget, there's a whole huge planet besides the US, Europe, Russia and China. Who is going to nuke Botswana?
And fallout depends on wind currents and distance from attack sites. And radiation also decreases with time, and there is potential for things like radiation hormesis occuring.
And as for the climatic effects, "this would do this, this and this" is far more better than "I say this would extinct all humans!!!" It is something that depends on a very wide range of factors.
It is theorised that the [ame="http://en.wikipedia.org/wiki/Toba_catastrophe_theory"]Toba eruption[/ame], which caused a volcanic winter up to a decade long, with a global mean surface temperature drop of 3-5C, reduced the number of humans to down to about 10 000 individuals, creating a genetic 'bottleneck'. Yet here we are some 75000 years later, still surviving.
Over the years, thousands of nuclear devices have been detonated. The largest number of nuclear tests in a year has been over 140.
Of course: I am thinking in ecological terms. On the scale of things like bolide impacts- mass extinction events. Humans may survive, but the human cost would be absolutely horrendous, an undescribable magnitude of suffering.
But it goes without saying, that an outmoded nuclear weapon is not needed to prevent the "Chinese nuclear threat" to the US. Neither are gigantic, omnicidal stockpiles of weapons. This was born out of a Cold War arms race that no longer exists. All that is 'needed' to form an 'acceptable' nuclear deterrant is some 200-400 weapons, which is unsurprisingly the number of weapons that many non US, non Russian nuclear states are said to possess. Just enough weapons, to make the other guy using weapons on you, a blitheringly bad idea.
I am not sure where the 30 000 number comes from though. The number of warheads possessed by the USA and Russia at the moment is more like 20 000, and active warheads are a subset of the total figure.