Yes, that's a good point - the global cooling effect IIRC was largely based on the emissions from burning cities, not the direct effects of nuclear explosions. Still, in an India-Pakistan war there would be much less burning cities than in the hypothetical cold war turning hot, which would burn the urban areas of the whole northern hemisphere.

It's a bit weird to guesstimate about so horrible hypothetical events, but perhaps the consequences of such a war might be comparable to all the many cities burned in firebombing and otherwise during WW2 - which, again, did not trigger a global cooling that might threaten global agriculture.