Something I have thought:
-Wood were really common in shields but not in other parts of armor. Cloth or leather was pretty common, while the wood was not. Why?
The thing is, you can't move your body as you can move your shield carrying arm. I think wood is not going to provide good protection against anything besides some cutting swings of swords. Spears will simply penetrate through your body, which was probably one of the most common weapons being used.
Just think of it like that. Imagine:
1-A sword thrust against a soldier wearing an armor made of wood.
2-A sword thrust against a soldier carrying a shield made of wood.
In the first case, the sword will simply go through I think. In the second case, the sword will probably won't be able to penetrate through because the shield is not static in this case. Most likely the angle of thrust will not be 90 degrees in the second case as well. Besides, the impact of the blow will also push the shield back a bit. Against armor, there won't be such a movement. I couldn't explain it much but I hope you understood it.
I think that's why cloth and leather was mostly preferred to wood, in armors. I think a good leather and cloth armor will provide that protection against sword swings. But they are also more flexible for the wearer.
Steel is of course better in any case, maybe save for shields.
Plus, I think the wooden shields were also useful for "trapping" your oponents weapon. Imagine the case where your pick is stuck at your oponent's shield. Wood seems to be the perfect material for that.
I don't know much about the subject, but that's what my unprofessional opinion is.
