Several things spring to my mind.
On the downside: (1). Wood will have faults in it (shakes, knots etc). To a large extent the worst faults can be removed by careful selection, but one might go through a lot of wood to find something suitable, and what's invisible on inspection might cause you problems at 10g (2) It's not isotropic (i.e., its characteristics vary by direction). It changes shape a lot across the grain but not so much along it. This makes it complicated to design something that will endure temperature swings, because the structure will distort. (3) One piece of wood will differ considerably from another of the same type, so one would need to allow a lot of margin for variation between a test prototype and a flight model. (4) Wood is an organic material, so in the vacuum of space will outgas a lot of both water (which will cause it to distort because of the anisotropy) and oils, tars etc. Those latter ones will go and find something cold to stick to (so, if you have high-precision optics, or cooled detectors, as we used to use when I did space science for money), it will seriously degrade your payload performance.
On the upside, (1) As noted above, wood has been used as a re-entry heat shield before (by the Chinese as far as I know, and an earlier commenter has mentioned the Russians). That's because it conducts heat poorly and actually (if hardwood like oak) chars relatively slowly - oak will take about an hour to burn through one inch. (2) Often what one struggles with structures is not strength but stiffness, and for the same weight, wood is pretty much as good as metal.
Biting the hand that feeds IT
