EDIT: as the sibling comment observes, burning the tree cannot be "awful", as all the carbon from that tree came from the atmosphere. Growing and burning a tree is the epitome of carbon-neutral thing to do. Now, burying a tree may have a positive (non-neutral) effect.
If it gets covered, and spends time in a cold, anaerobic environment, there will be nothing to return it to the atmosphere. Decomposition can eventually stall out entirely, allowing it (given enough time and compression) to form coal or oil.
I'm very interested in wood gas pyrolosis, a process that pulls burnable fuel from wood and produces almost pure carbon as a byproduct. The gas could be used to generate electricity or heat, and the carbon could be buried in old mines. I suspect the economics just aren't there for it yet, (or the process doesn't scale to the numbers we'd need for large scale de-carbonization).
The biosphere is a closed cycle, we cannot probably use it to store carbon away by means of its own mechanism. Main problem is that we are adding new fossil carbon into it every day.