yea thats what i have in mind heirlooming arrows, and instead of katana i have nomad sabre (looks better)
If you really want to nobody is stopping you. But keep in mind that since you're not gonna have many WPF/Skill points left over b/c of your HA build, you might want to use fast swords with a longer length and more damage as well e.g Katana (bit costly though).
Is the Sarranid a better choice than the Courser for Horse archery?
Since the only thing better is the horse maneuver, I would say no. Although a HA does need high maneuver, I would just stick with the Steppe Horse if thats your only reason to choose it over the Courser. The Courser can take more damage, and is faster for quicker escapes.
What are the best stats to pick in order to do really good on horse archery?
You're going to need the Power Draw, Horse Archery, Riding, and Weapon Master. For attributes, you're going to need at least 12 Str (Khergit bow) or 15 Str (Strong bow, a bit more dmg) and stacking Agility in order to get HA, Riding, and the WM skills high.
Watch your back-right side, 45 degree angle is where you can't shoot, I believe.
Actually, in-game Ive seen that I can turn almost 90 degrees on the left while mounted...weird