IRL, barding is the armour that warhorses wore, to prevent cavalry charges being suicidal when the enemy have pikes or longbows. Barding is definitely in-period to an extent, as it was used by a number of ancient cultures such as Rome in the form of cataphracts, though this was scale armour, not plate. It's not outside the in-period tech capabilities to make plate barding, but it wasn't really done IRL until just a little after the cutoff point AFAIK.
It would seem like a suggestion that should be implemented after mounts are a thing for players, at least in adventure mode, but there's no real reason not to allow all warbeasts to wear some kind of armour. It would certainly make them more useful and reliable as actual defenders (and much more fun as attackers when invaders bring mounts and warbeasts), because currently they're little more than meat shields unless you either catch/trade for giants, or (somehow) stuff all 50 of them into a cage linked to a pressure plate/lever. It shouldn't make them too powerful since they still only have their natural weapons, with the exceptions of megabeasts, adamantine barded fully grown dragons will be basically unstoppable, Armok help you if you forget to replace dead animal trainers. Maybe no barding that provides full coverage? Just to keep things balanced, and so having huge and terrifying war trained guard beasts doesn't make fortress defence boring.
Bonus: If barding is applied via the animals screen, and can be applied to caged hostile animals, gladiatorial combat can become much more fun.