Your Archers Have a Bad Time
So my first thought is, "There's no way you could convince archers to do this." Why? Because of three things:
- Being up in a tree does nothing for them, archery-wise. You can't take a proper stance, because you're on a tree limb and worried about falling. You can't have massed volley-fire, because the tree branches block LOS and the archers are too dispersed. You COULD ambush people (even in urban fights where we 'expect' the Bad Guy to be in upper-story windows people don't look up. That tendency will only be exacerbated in a world where essentially none of your soldiers routinely think about "upstairs.") But the problem with that is....
- You can't decisively destroy the enemy force. The Tutenbourg Forest, where German tribesman slaughtered 3 Roman Legions, is a textbook ancient ambush... that lasted 3 days. Your archers are up trees. You wait for The Perfect Moment. You fire! Loose all the arrows! (probably not at your 12-shots-a-minute max speed because your archers are all up trees) Your accuracy.... isn't great. Because it's bow-and-arrow at armored targets, in the woods, with lots of branches in the way. Plus ancient armor is DESIGNED to stop impacts from above anyway. Still, the enemy is disorganized, maybe some leaders are down, and they quickly fall back out of bowshot. Now what? Your archers clamber down 50ft of tree to chase after them? Not fast they don't! The enemy has plenty of time to reorganize themselves. If they even flee, which if they're smart they won't because...
- A guy in a tree is a dead man, one way or the other. There is a Very Good Reason you don't see this in real life beyond the very occasional lone sniper. That's because being in a tree might be great concealment, but the second the enemy knows you're there you're at a HUGE disadvantage. If the enemy sets fire to your tree, then what? Or if he simply keeps a watch on you from a safe* distance. *safe being either out of bowshot or within bow-range but under a pavaise of some sort.
Once the enemy knows you're there, exposed, on the side of a tree, it's not too terribly difficult to have their own smaller force of archers outflank you. The enemy on the ground has shields, you have a hard-to-move-around-in tree. You get shot. you die. Or they go around you, you starve to death, and die.
It's point 3 that really toasts this plan. A small ambush of 10ish guys up trees to kill 10 other guys? MAYBE that works out. But armies? You want me, Joe Archer, to stay in a tree, where I can't run away if the plan goes awry, and shoot arrows? Of which I have.... how many? Not enough to hold my position if THEIR archers kill my 6 buddies. There's 6,000 enemies. What if a larger-than-average force comes at my position? I can't fall back, I can't kill them all, I probably can't even surrender fast enough. No sir, ain't doing it!
What you COULD Accomplish
So how do I fight an army of mostly-infantry with a force of archers in a woodlands environment? Simple. I DON'T. Not a smack-down drag-out fight anyway. Can't meet them in a pitched battle, arrowstorms don't work in woods, and without a line of infantry to support me I can't hold a position. So I send half the archers home, they're just mouths to feed and medieval logistics are murderous. Instead I harass their foraging parties, kill their scouts, have 6 guys fire 2 arrows each at the head of their column then have them meld back into the woods, just for another 6 guys to do the exact same thing 10 minutes later. Always always ALWAYS have a fallback position. Have other archers kill or drive away all the game in the area near where they're traveling, then have yet more archers kill the oxen pulling their supply wagons. Find a couple axes? Great! Chop down trees to slow their passage. Which means it takes yet more supplies for them to traverse said woods. The enemy starves, gives up, and goes home. Or starves, stays put, and is slowly attrited away to nothing.
A Note on Arrows
A consideration when thinking of medieval archery is penetration of your arrows. It's not like Total War where your maximum range is maximum deadliness and the only difference is accuracy. The force of an arrow drops off DRAMATICALLY with distance. To the point where, if your bow can shoot an arrow 100 meters (totally arbitrary number) You're only really dangerous to a man at 50 meters (any further away and a quilted jerkin is likely to stop your arrow) and it's only at 20ish meters that your arrows are accurate and powerful enough to do things like "kill a guy in mail with a shield and a helmet" reliably. Even shooting downwards distance dramatically lowers punch. For more, see Armor punching myths