When a tree is burned it releases Carbon Dioxide (CO2) that the tree has absorbed over the life of the tree through photosynthesis.

Another advantage of wood, unlike fossil fuels such as gas or oil is that it is an ecologically renewable resource and will not run out. Very soon in the the near future you may be heating your house with sustainable wood or similar biomass technology.
Some tips for climate-neutral heating:
Choose a stove that meets even the most stringent environmental standards.
Regularly inspect the flue.
Only burn clean and dry firewood, with ideally less than 20% moisture content.
Ensure there is sufficient ventilation for effective combustion.