The main air pollutants in wood smoke are particulate matter (PM), carbon monoxide, carbon dioxide, nitrogen oxides and a range of other organic compounds like formaldehyde, benzene and polycyclic aromatic hydrocarbons.[1][2]
Using reverse-cycle refrigerant heating (or 'heat pumps') is probably the least worst polluting method of heating. Modern heat pumps can generate (well, move) four times more heat energy than used to drive the pump[3], with the added benefit of moving the source of pollution away from populated areas, or being carbon neutral via window, solar, hydro, geothermal.
1. http://www.health.nsw.gov.au/environment/factsheets/Pages/wo...
2. https://www.environment.gov.au/resource/wood-heater-particle...
3. https://en.wikipedia.org/wiki/Heat_pump#Performance_Consider...
If you burn coal for power at 40% efficiency and run a heat pump at 400% efficiency that's only 1.6x heat gain ignoring transportation losses. Drop that heat pump down to 150% efficiency and heating oil can become a better option.
In most areas using solar thermal heaters with backup resistance heating is actually the best overall option. But, in most of Alaska heating oil is much more viable.
I think you're right about the cleanness of heat pump systems. Unfortunately they do not have the libertarian freedom flavour of a wood fire.