It is carbon neutral but in this case its a bad thing.
Because the tree was the actual carbon neutral part of it.
Trees are one big 'sink' of carbon, during the growth of the organism it gains a lot of carbon that is taken from the atmosphere, burning it releases a great deal of carbon.
Killing the tree by cutting it down for firewood and burning it, not only are you releasing the carbon within its wood, but you are also responsible for that tree no longer being able to store more carbon in future.
The best thing would be to leave the tree until it died naturally, but as IHateSprouts said, rotting wood would produce methane, which is more harmful than carbon dioxide to the ecosystem. So that the best way to do it would be burning dead wood.
That way you ensure that the carbon actually stays in the carbon sink for longer and it was able to store the most carbon.
( 6821isnotmyPIN Bored cig., Wed 10 Nov 2010, 15:36, 2 replies)

And then plant a sapling for each tree that you burnt

(Reverend Fister "a disciplined fuckwit", Wed 10 Nov 2010, 15:57, closed)

Wood supply
Most of my wood comes from either tree surgeons (I know 2) or sustainable suppliers. I also get oak and larch offcuts from a woodframed house building company. And they do indeed replant what they chop down except the tree surgeons obviously.
(sittingduck Attention seeking, bullshitting fuck-knuckle, Wed 10 Nov 2010, 16:58, closed)

I've never heard of anyone cutting a tree down for firewood
The logs I burn are from pruned trees and those felled for other reasons (e.g. they were diseased and unstable). Tree surgeons are always lopping branches and tops off trees and that's what gets turned into firewood round my way.

Of course, if someone is going round clear-felling trees purely for firewood, that would be environmentally dodgy.
(IHateSprouts is baking a huge pie shaped like an enormous pie, Wed 10 Nov 2010, 17:47, closed)