The scariest scenario in Asia right now is: China attacks Japan (e.g. invades the Senkakus, or even accidentally kills some Japanese soldier in one of China's frequent reckless acts of attempted intimidation, like flying dangerously close), the Japan retaliates, the China escalates, then USA intervenes, and somehow USA and China end up in direct armed conflict.
But even there, China and USA have directly fought each other in a war (Korean war) and nobody pulled out their nukes (though China didn't have them yet iirc). The USSR and USA were always invading somebody or other. The nuclear Armageddon scenario is probably a lot less likely than feared--whereas I think the possibility of a nevertheless-vey-bad war in Asia is broadly underestimated.