As long as the wood is locally havested, minimising carbon released in processing, and from a sustainable/managed source, then it's pretty good. Nothing is perfect.
Trouble comes when firstf is clear felled and not managed. Also I've read that a rotted tree doesn't release all its carbon, a significant amount ends up as long term carbon in the soil. So burning is worse, and felling can, if done poorly, lead to soil erosion or degraded quality so carbon in the soil can be released. I'm not saying burning wood is bad, I don't think it is, but we should be cognisant that it's not entirely straightforward....
Nothing is where the environment and climate are involved.... It's very complex.