Average teamfight lasts around 20-30 secs, and that's the only time you can catch the arrow, and if you aware of your position and your movements you won't get every single shot in your horse's head, so you can hit enemy inf like 5 times before you get dismounted and that's how you win the fight as cav. These calculations only work if enemy archer is focusing your horse the whole fight, and if he do so, he's a bit useless cause when your horse get hits, you still can kill enemy inf and the only thing enemy archer doing is trying to dismount you and not get any inf headshots.
From your messages I see you think that horses should be unkillable as if archer's won't deal horse damage, there won't be any reliable damage to enemy horse cause in close fight all inf switches to melee weapon which, as you just said, deal around 20 dmg to the enemy horse. I know you want your class to be op so you can enjoy your gameplay, but the game needs some balance. Cav is not a premium class, it does it's thing and a good cav can totally rekt enemy team even when there's an enemy arch shooting, no matter how good he is.
As I said before, archs were always good against cav and cav were always good in teamfights, and that's how game works. If you think cav should take no dmg from an archer and should be able to easily kill him, you just have a biased game sence.