I'd rule that an animal with the respective combat training does not need the armour proficiencies... since none of the warhorses or riding dogs in the MM have these proficiencies.
Unless it's used as a mount, in which case you could use your ride skill to avoid it getting hit, once per round though, but still that's after you know whether it's getting hit or not.
Agreed. My mount still wouldn't wear anything over chain shirt because of the Speed decrease, however.
In this case, if you're doing most of the damage, the fact that your mount has a -2 to hit isn't that horrible. It's worth a feat if you're not planning on taking anything else, but ... I'd still say go for the leather armor, or at worst, masterwork Studded Leather (for the Ranger).
So imagine this:
I have a 6th level druid who will probably have a wolf companion for at least another few levels as well. Currently it's AC is 20 because for one of it's feats I gave it Improved Natural Armour and the other natural armour/dex bonus from behing a 6HD animal companion.
So if we add Leather Barding +1 and I cast barkskin the wolf will now have and AC of 26!!!!!