Are mounts proficient in armour (barding)?

Mounts can be given barding to duplicate the effect of armour at 4x the cost. However, barding makes no statement about armour proficiency, nor does the stat block for some of the more obvious mounts (Riding Horse, Warhorse, etc.).

If a mount is given barding, is it proficient in it? If not, how is it possible for them to gain proficiency?

The penalties for wearing armour without proficiency are no spellcasting and disadvantage on ability checks, saving throws, and attacks that use Strength or Dexterity.

Assuming they are not proficient, do mounts with barding have disadvantage on Strength and Dexterity -based ability checks and saving throws?

And finally, non-humanoid creatures are not explicitly stated to use either Strength or Dexterity in their attacks, but I would assume physical attacks have to use one of these two, so:

Assuming they are not proficient, do mounts with barding have disadvantage on attacks?