what if you are on attack though? You won't have the height advantage then.
Well, if your concern is archers, you could try to pin the enemy center with spears and gallowglasses, and try to come around the enemy's flanks with cav or some fast infantry (most of the Irish infantry is pretty nimble) and try to drive off or scatter the archers. This will also put you behind the enemy's center, which is also very good.

You could travel through woods as much as possible or wait for rain, as katank suggested (indirectly).

Or you could accept casualties from archer fire and try to crush the enemy's main line, using javs to kill armor or weaken spear units, then finish them off with gallowglasses and go after the archers last. This requires packing plenty of troops though and may not be desirous (especially with a cowardly AI that will run if fighting even slightly larger numbers).

The easiest (and probably least helpful) answer to that question, son of spam, would be to not find oneself on the offensive.