Wood Burning is not Climate Neutral
Woodburners among others often assume that if they burn a tree somewhere somehow a replacement tree will be planted and when it grows to the same weight as the tree they have burned, then the amount of carbon dioxide that was emitted by burning the tree will have been reabsorbed by the replacement tree. That is what they mean by carbon neutral. Unfortunately, they then conclude that wood burning will therefore have no effect on climate.
That conclusion is unwarranted because there are more climatic effects involved than just the release of carbon dioxide from the actual wood burning. Among them is the consumption of fossil fuels to cut the tree and chop it up as well as in the trucking of the wood to the burners stove. Clearly that consumption should be included in the carbon balance.
Of great importance is that fact in addition to the gas carbon dioxide some of the carbon emitted is in the form of microscopic soot particles which absorb sunlight, heat up and thereby reduce the cloud formation which then allows an increase of solar radiation to reach the Earth's surface increasing the temperature. The effect of soot particles is thought by some to be the second most important cause of global warming.
Climate change effects which occur within the next decade or so will be crucial. Many climate change scientists think that we are perilously close to the tipping point where changes to the climate will be irreversible, i.e., catastrophic process will get to the point where they cannot be stopped. We simply don't have the time for new trees to grow.
We should concentrate rather on the notion of "climate neutral" which applies to processes that do not affect climate change over a fairly short time span and put the burden on the burner to recognize that his activity over a short period of time, like a heating season, will exacerbate the problems of global warming as well as harm public health.