3 HA is defiantly viable as a HA
Sorry sir but I must disagree with this. HA is a pivotal skill for said class.
How important is the horse archery 4, Is it more important than PS 5?
If you want to be a proficient horse xbower then yes, I believe it is. 4 Powerstrike will be a little shitty but if you use a loomed Military Sickle and aim for the face you will be surprisingly efficient
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Why do I need riding 8 in that build and is there 0 Athletics?
Well good sir,
it might be pretty awesome if enemy cav is chasing you: just ride in front of them and shoot their horses 
Low riding skill ranged users often get smashed by melee riders due to the fact that HA/HX should use high maneuver horses which consequently, are slow, especially when compared to a +3 courser using lancer with 6 riding.
In my experience athletics was not so important; due to high agility you will not be sluggish on the ground but it is more important to retain accuracy and horse skill.
I presume I should use the light crossbow and military sickle what other clothes and equipment would you recommend?
Indeed, loomed light xbow, steel bolts and military sickle will mean you do quite reasonable damage, especially with headshots.
Well, I believe the order of wpf penalty by weight is: gloves, head, shoes then body.
I would use leather gloves, a helmet of no more than 1 weight (I use Skullcap because I like the look of it hehe), Eastern Leather Greaves for their armor/weight ratio and lamellar may be a little heavy, I used Heavy Aketon.
This armor served me well on my HX and I recommend any similar armors; choose what you like but remember, this weight is good
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As for the horse, you want something that has high maneuver. Arabian Warhorse is the best horse for this but it is indeed expensive and you will need to get to a fairly high level before you can actually ride it. Steppe horse still has good maneuver but the speed is quite bad and it is weak like all maneuvering horses, however it is cheap and requires low riding skill. Desert horse does not maneuver as well and is even weaker but is faster and has slightly better charge but again, requires high riding skill.
I hope this helps ye.
