In war, the economy does not slow down. It is turbocharged.

A nuclear war could counter global warming by triggering a nuclear winter but the actual effects are very uncertain. Basically, for a nuclear winter, a lot of “dust” needs to be lifted into the stratosphere. Those huge, multi-megaton bombs that they had back in the day caused a mushroom cloud that rose all the way to the stratosphere. Today, smaller, more precisely targeted bombs are preferred. It also depends on how combustible the targets are. No one is really quite sure what the climate effect of nuking a city is.

A substantial reduction in the human population would largely end the burning of fossil fuels and trigger reforestation; removing CO2 from the atmosphere. Ultimately, I would expect WW3 to greatly mitigate global warming.