Not sure what your gauge for bad is, but low-temperature burning of coal and wood, which is what you get with cheap wood heaters, produces smoke that is definitely polluting and unhealthy. You can get a wood burner that re-burns well and is very efficient and burns the smoke so completely that you mostly get CO2 and water vapor coming out of the chimney, but they're expensive.

Care to share more about trash burning? I'd be surprised if people living in Krakow or Warsaw commonly burn trash.

The traditional Polish categories of sorting rubbish is „to the burner” and „to the forest”, optionally „to be burned during the day” and „to be burned during the night”.

They burn all kind of shit in very inefficient stoves, modern wood burning stoves are pretty clean