You may have nailed it. Coal fired heat?
A faulty gas heater could do it also. Many years ago, my girlfriend and I lit the gas wall heater on one of the first cold nights that winter. We had really nasty headaches the next morning, and the heater sounded different, so we shut it off and called an HVAC guy. He told us that the heater’s manifold was cracked in such a way that CO was being released into the house, and that we were lucky to have woken up at all. Good thing that place was so drafty.