I think the domestic heating use is a drop in the bucket compared to commercial extraction of peat for export, or historical use for electricity generation.
I've only so many shits to give, and people heating their homes doesn't rank.
On cold mornings you can see the wood smoke hanging over the town of Taos New Mexico. It's easy to see even a little bit of haze in the otherwise crystal clear air. Taos is in general a very environmentally conscious place. The KTAO radio station has been solar powered since the early 1990s. It also has a significant population of low wage tourism industry workers.
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.