A/C for cooling is one of those things that highly correlates with the availability of solar power.
So your assumption that they are running on coal is suspect.
Heatpumps running in the winter are a more pressing concern, since those are highly correlated with the unavailability of solar and therefore often run on coal or gas (unless wind or hydro is available)
Even so, burning gas in a power plant and then running a heat pump is more efficient than burning gas to warm a house.