It would be really, really, really, really really bad, and not just for the region but for the whole world.
Simply put, soot would block about 20% to 30% of the Sun’s light, globally. That’s a decrease of about 30W to 60W per square meter of the Earth’s surface. For comparison, the 1991 eruption of Mount Pinatubo caused a decrease of 4W per square meter. The result would be a 2°C to 5°C (about 4°F to 9°F) global cooling. Temperatures would reach their lowest after about three years and maintain that level for another four years. Getting back to previous temperatures would take over a decade.
The cooling would slow the hydrologic cycle and decrease rainfall by 15% to 30% percent globally, with impacts varying in different regions. In India and Central China, for example, precipitation would drop to nearly zero. The Northeastern and Midwestern United States would see a decline of 50%.
The temperature, precipitation, and sunlight change would obviously impact photosynthesis on land and in the ocean. The model estimated a 15% to 30% drop in growth on land—known as Net Primary Productivity—and a 5% to 15% drop in the ocean.
If global warming gets really bad, maybe we can just blow up a nuke or two on some out of the way continent. Antarctica won’t work because there isn’t much combustible material there. So no, never mind, I never said that.