Hmmm,
As mentioned already, a paladin's warhorse, or any warhorse for that matter, doesn't need a feat to wear plate barding.
Furthermore, I don't think the PHB says anything about animals needing a feat to wear armor. It just says that you can fashion armor to fit them. And, as mentioned above, they can be trained to wear it.
So, although my gut reaction is to say, "they need the feat, after all, humans are smart enough to put armor on, but they still need to spend a feat to know how to wear it effectively." it seems that the rules are against me. I can see the reasoning in it too.
For one thing, are animals even smart enough to realize that there is a right way and a wrong way to wear plate mail? I doubt it. They just wear it. I suppose that means they should get the nonproficient penalties. And, in time thy might become comfortable with it (becoming proficient??).
So, now I'm argueing with myself about it.....
I don't know...
No matter how I look at it, the book suggests that they don't need a feat, but I really think they should, or suffer penalties.