People heating their homes can be very sigificant. In the UK ~15% of all its territorial GHGs come from heating with gas: actual CO2 from the home boiler flues.

CO2 from small amounts of rural home heating is probably not the big thing to be worried about, especially if local recent biomass, eg wood from forest management. But there are still nasties (PMs, biodiversity losses, etc) to be considered and that should be dealt with in due course.