You don't need to disengage when riding a mount since you're not using your movement, action or reaction to move. However, if a mount provokes an opportunity attack, the enemy can choose to attack either the mount or the rider, so you should command the mount to disengage.
You can avoid provoking an opportunity attack by taking the Disengage action. You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. For example, you don't provoke an opportunity attack if an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy.
Controlling a Mount
While you’re mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently.
You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training. The initiative of a controlled mount changes to match yours when you mount it. 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.
An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes. It might flee from combat, rush to attack and devour a badly injured foe, or otherwise act against your wishes.
In either case, if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount.
Cunning Action lets you disengage. Your mount is a separate creature. It needs to use its own action to Disengage on its turn before it moves.
And it requires an action to tell your mount to do this?
No, it is an independent creature with its own turn (initiative matched to yours) that can move and take actions. That action could be disengage, you merely need to tell your mount what to do(not an action).
Pact of the chain and beast master familiar/companion are combatants and are, under certain conditions allowed to attack. A mount can only take the Dash, Disengage, or Dodge action.
Can I use my cunning action to disengage if I'm on a mount? Can I tell my mount to disengage?
You don't need to disengage when riding a mount since you're not using your movement, action or reaction to move. However, if a mount provokes an opportunity attack, the enemy can choose to attack either the mount or the rider, so you should command the mount to disengage.
This is all covered in the combat rules.
The Forum Infestation (TM)
But can I control my mount to disengage as part of cunning action? The way they say it makes it seem like it requires an action to control your mount.
Cunning Action lets you disengage. Your mount is a separate creature. It needs to use its own action to Disengage on its turn before it moves.
The Forum Infestation (TM)
And it requires an action to tell your mount to do this?
No, it is an independent creature with its own turn (initiative matched to yours) that can move and take actions. That action could be disengage, you merely need to tell your mount what to do(not an action).
Jesus Saves!... Everyone else takes damage.
...wait really? I thought that, once you mounted it, it followed like the rules of Pact of the Chain or the Beast Master Ranger.
Pact of the chain and beast master familiar/companion are combatants and are, under certain conditions allowed to attack. A mount can only take the Dash, Disengage, or Dodge action.
Jesus Saves!... Everyone else takes damage.