As far as I can tell, there are hardly any rules on this subject. All we have is:
PHB, chapter 5, page 144: (generally armor)
Armor knowledge. Anyone can put on armor or put on a shield
to an arm Only those who know the armor know how to wear it
it effectively, however. Your class teaches you with specific knowledge
Types of armor. If you wear armor with which you have no abilities, you are
have a drawback with every skill check, save, or attack roll
this includes strength or skill and you can not cast spells.
Conclusion: Anyone who wears armor must be competent or face the consequences.
PHB, chapter 5, page 155: (on cash as equipment, price)
Barding Barding is an armor that covers the head, neck and neck
Chest and body. Any type of armor displayed on the armor table
This chapter can be purchased as cash. The cost is four times
Equivalent armor for humanoids, and it weighs twice as much.
In summary, you can armor an animal and the price is four times that of a normal armor.
PHB, Appendix D, page 310: (Variant rule especially for Warhorse)
Variant: Warhorse armor
An armored Warhorse has an armor class based on the type of Bards worn
(For more information about Bards, see Chapter 5). His armor class includes the
if necessary the modifier "Dexterity" of the horse.
In summary: A war horse can wear armor. Warhorse, unlike riding horse. Since this is a deviant rule, it implies that without the deviating rule, all beasts (not just warhorses and war dogs, war elephants, etc., as I suppose) can bear bards.
But do you need knowledge? In accordance with the general rule for armor strength listed above; Yes, How would an animal acquire such ability? Besides, we are not told what the difference between a riding horse and a fighting horse is and whether / how the first one can become the latter.
However, if the RAW is missing, we just keep rolling. The spirit of the game was always "make up as you go". So I would suggest the following: A non trained warrior does not control the armor. A war-trained mount is. I believe that this is relatively consistent with the above rules.
We also have to set some rules for training a warbeast. Do you say rigorous training for a month or two in the hands of a specialist?
Yes, and that's what I mentioned: a lawyer could argue that bards and armor are two different things. I would say that it is the same with different names, depending on the wearer.