Nuclear war happened in the Star Trek universe. “Encounter at Farpoint” talks about the Post-Atomic Horror. Star Trek: First Contact tells us 600 million dead. But where?
Asia and the Pacific Rim? Gone, reduced to radioactive slag. That makes sense, given what Q showed us of the court from the Post-Atomic Horror, and the fact that there doesn’t seem to be anyone of Asian descent in the 23rd and 24th centuries (and those that we do see clearly hail from North America–Sulu from San Francisco, Harry from South Carolina [I think], and Hash [from NF] probably from Georgia).
North America? Europe? Largely untouched. San Fransisco looks a little different, the Eiffel Tower still stands, so we know these cities didn’t get hit with mushroom clouds. (On the other hand, a lot is going to depend on the yield of the weapon and whether it’s an airburster or a groundburster, so these cities could have taken a nuclear hit.)
Something to remember, though. A nuclear war in the 21st century won’t render a place uninhabitable; you could in time (a decade at most) return to the area and resettle it. (Brendan DuBois’ kickass alternate history Resurrection Day deals with that very point.) So, just because Asia is a radioactive parking lot in 2060 doesn’t mean no one’s living there in 2360.
Essentially, the point I’m trying to make is this: a nuclear war doesn’t necessarily have to be global. Something beginning in India, Pakistan, or China wouldn’t necessarily involve everyone. (Though I would question a situation where India and China were exchanging nukes and China didn’t take a pot-shot at Russia or the United States just to get one in.) The Cold War mentality is that a nuclear war would affect everyone , and while there would be some global cooling in the short term (since it looks like Carl Sagan overstated the nuclear winter hypothesis), a limited nuclear exchange is more probable in Trek‘s history.
Or at least, that’s the way I see it.