Ash was the traditional wood for spear shafts—being light and very springy—so as to absorb the bending force applied when the spear point engaged the target armor without failing.
Axes, other handled weaponry
The favored Early Medieval wood for shafts was in Old English called 'corntreow' or 'gatetreow', this translates as cornel cherry. As this is from an english text and the cornel cherry is thought to have been a 16th C. introduction the dogwood seems more likely.
Hickory was for axe handles, a very tough wood that absorbed the shock impact forces generated in use.
She also talks about plants as aids to healing, as wards against sorcery, and their use in heraldry. She finishes with a list of ideas for incorporating some of the ideas in your campaign. I love to use this sort of stuff for color and character, such as when I describe what happens when a character uses non-magical or herb-based healing skills, or discussing the weapons and equipment of soldiers and enemies.