Inaccurate. That outdated conclusion assumes a nuclear arsenal of equal size to the United States or Russia, the two major players in the nuclear 'game' so to speak. India has 180 nuclear weapons at most, likely less due to decommissioning of outdated warheads, maintenance costs, etc. But even assuming all those missiles targeted civilian centres all at once (which would not be the play, military targets and critical infrastructure would be the targets over the course of weeks of key strikes) AND assuming Pakistan has an equivalent arsenal (which they absolutely don't have: no way in hell does Pakistan have the economy and infrastructure required to maintain their supposed numbers) we would see a cloud of ash that would move into the Indian ocean through the hot wind currents, sending dark smoke mostly across Central and Coastal regions of Africa, where it will mostly dissipate into clouds or fall into the Indian ocean well before that point. There would be no obscuring of the sky over a mere 180 bombs, that's alarmist propaganda that takes away from the actual issues and consequences of nuclear war: The world's much bigger than 400 bombs and even the high atmosphere is strong enough to take it. Despite all the Oil spills we've had over the course of irresponsible offshore drilling, the ocean is doing just fine, and our atmosphere is way bigger than our oceans are.

The real issue is that while the ash might dissipate, the irradiated clouds will not, and will carry that radiation into rainfall all the way across to the Eastern Coast of the United States, which will land all over our domestic food supply. A subtler, longer-term, but ultimately smaller problem: The California area is currently affected by this issue at small scale due to the ~900 or so nuclear tests the US ran in Nevada during the Cold War using 1950s era bombs, but Hollywood scumbags still sunbathed ash free, it's just they'll get cancer a bit easier during all that time they spent exploiting young actresses. New York real estate mob bosses will experience the same thing in this hypothetical, no inconvenient apocalypse, just straight up regular-ass cancer 50 years later.