According to the Player's Handbook, pg. 198:
Controlling a Mount
While you're mounted, you have two options. You can either control the mount or allow it to act independently.
You can control a mount only if it has been trained to accept a rider. [...] It moves as you direct it, and it has only three action options; Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.
This does not specify if the actions listed:
- are the only options a controlled mount may take in the round, OR
- are the only options a controlled mount may take with, explicitly, a standard Action.
Can a controlled mount make an Opportunity Attack if an enemy moves away from it?