If your Siege weapon can destroy an inconveniently placed arrow tower, it might give you the much needed safe spot to slowly destroy enemies with your arrows.

There is still hope to defeat an archer-heavy defending stack. First, you can lure the mobile shooters units out with Archer duels one by one. This works great with the unpatched game, but after patches there is some difficulty (they still chase out sometimes).

Another way involves a lot of patience. The AI units have limited arrows like you. So you can purposely move any unit within the enemy's firing area, and as soon as you see arrows leaving their bows, quickly run away to move outside of their range. The enemy's arrows cannot trace you like guidede missles. They are fired assuming your unit keeps the current momentum. So theoretically you can exhaust all arrows from all AI untis one to two volleys at a time. Then they are just sitting ducks! This also works when you are the attacker on the field. But the AI will charge toward you when their ranged power drops below you by a certain extent.

The patches also weakend the effectiveness of arrows. What you used to kill with 3 units of Bow Ashigaru now might take 5. This could work against you, but it also helps you to cut down loss when you try to exhaust their arrows.