Strictly wood is NOT a carbon footprint because it's part of a short-term carbon cycle (in <100 years it's already back into trees).
Until recently I lived in the boonies and ONLY used wood for heating.
The biggest problem with wood: you have to constantly manage/regulate the fueling and heating - even the best stoves need to be refilled in 4-6 hours when the temperature is below 10C. Further, you only get this if you've aged (dried) the wood for 2 years first. Newly cut wood is 20-30% water and the heat of vaporization to steam radically reduces the heating value of the burned wood.