So far as I know, Armor on a Centaur is 'two phase'... meaning, that the upper torso is covered by 'normal' armor types, but... The lower 'Equine' (horse) body of the Centaur requires 'Barding', which is armor for a horse. Barding costs four times the cost of whatever armor type of the upperbody, and weighs twice the upper torso armor's weight.
Thus, Studded Leather: AC 12 + DEX, 13 lbs, 45 GP. And the same Barding would cost be: AC 12 + DEX, 26 lbs, 180 GP. For a total of AC 12 + DEX, 39 lbs, and 225 GP cost.
As for the question as to Arcane Armor and its protection, yes. The AA does extend to all four legs of the lower body.
Centaurs can choose to wear 'standard' armor, 'barding', or both, But only both counts as 'fully armored'. Wearing either, or both types of armor does not affect movement, so the Centaur thus armored would still have its full 40-foot movement rate.
Addendum: A Centaur can wear both a backpack, AND saddlebags. Saddlebags hold more (between the two of them, and always in pairs) than a standard backpack. A backpack's weight limit is 2 GP cost, 5 lbs weight, for 30 lbs capacity. Saddlebags are 4 GP cost, 8 lbs, for 40 to 50 lbs capacity. Saddlebags are NOT a 'saddle' and should be envisioned like saddlebags seen in old Western movies, mounted behind a saddle on a horse. A Centaur might wear a saddle and allow a small to medium-sized person to ride them. The rider can fight from the Centaur's back, and Centaur will fight 'normally' with or without a 'rider'. No bonuses are given for such combat, since the 'mount' and 'rider' are not trained to work with each other.
Just a few thoughts on the subject.