If you bring the king the axe and letter, he should tell you about the armour.
VERY BIG SPOILER ON DRAGON ARMOR SETStand close to the tree, open a barrel of tea, and toss it at the tree. Save first, in case you don't get the hang of it before killing the tree (I moved a couple of open barrels, not realizing that would set them off, but still had one left to kill the tree with).