My champion courser usually dies in 3-4 arrow hits unless it is hit in the head which always (or almost always) causes it to die instantly.
And I haven't noticed much difference with armoured horses, seems they die from 1 hit to head just as easy as unarmoured ones which feels a bit wrong. All bows but longbow makes piercing damage so that shouldn't happen so easily to armoured heads.
First, yep, i guess you wrote it wrong, so it's cutting instead of piercing.
2nd, the "seems" is indeed what it seems like, a false impression. No longbow with 6 PS can insta 1hit an armoured horse in the head.
Also, it's funny how all thoses "usually 3/4" arrows, and "almost always one shot in the head" ALWAYS only take in consideration longbow with 6 PD, and not the strong bow with 5 PD wich deals quite a bit less damage.
And again, i'm sure you get focused by xbows too, and thoses sure deal way more damage than any bows, with a slightly better accuracy at mid range.
Back to topic :
+1 to horses should have their free will, the percentage of free will is really low and would only make it more interesting. Plus it wouldn't bother at all the dedicated cav.
+1 for buff armo hp, if La MAkina's two ideas are added. And only slow the horse once it has taken at least 50% damage, that way, cav can still ride a bit to dangerous zones at their normal speed.