wood fires are fairly dirty in terms of smoke, soot and tar; but the carbon emission is about net-nil, because the trees sucked the carbon out of the air to grow, all you are doing when you burn it are putting it back where it came from over the last 10/20/whatever years.
If, for every tree you burn, you grown another of the same size, there is no change to the carbon load in the atmosphere.
p.s. if you didn't burn that wood, but left it to rot, the carbon would be returned to the atmosphere anyway as the wood broke down and was eaten by insects and funghi.
If however you carried it down a dry coal mine and left it there for a few million years, the carbon would be locked up until someone dug it up and burned it.