In the PHB (p.198) mounts are either controlled or independent.
Controlled mounts have only three actions, move, disengage, or dash. Combat is not an option.
Uncontrolled mounts can take whatever action they desire independent of their rider.
It seems somewhat clear how intelligent mounts might act. For example, a dragon could be told to attack a particular foe and it just might obey your commands.
But what about trained mounts like warhorses with limited intelligence? In actual historical battles, war horses could “attack” opponents using the 5e equivalents of the “Shove” action or “Shove Aside” action or “Trample” as in previous editions of D&D. (Trample seems to apparently no longer exists as we are unable to find any references across PHB, MM, or DMG.)
In 5e if you take “control” of a mount, it cannot take those Attack actions.
Given that, what 5e guidance is there for issuing commands to “uncontrolled” but trained mounts? Can one use the reins to direct a warhorse to trample an opponent or give more complex non-verbal commands like turn, charge and attack?
Most importantly, assuming these commands can be issued, what guidance does RAW give regarding how long those commands would take? Would these be considered actions allowable during one’s turn or would they take a Full Action or Bonus Action?