The initiative of a controlled mount changes to match yours when you mount it. However, this does not mean that they act on the same turn. The mount gets its own turn but the rules make it so that it acts on the same initiative count as you. Jeremy Crawford has clarified and agreed with this here:
Can a controlled Mount take an extra attack?
This means you can’t do drive-by attacks with Extra Attack on a controlled mount. The only way to use Extra Attack is on your own turn, so the mount would have to go first, move you into range, and ready an action to keep moving after you attack, but controlled mounts can’t take the ready action.
When does a mount move, it uses its own movement?
When mounts move, they use their own movement not that of the rider. Thus, when using a mount to move around, the rider is not using their movement, action, or reaction and thus cannot provoke opportunity attacks.
When does a controlled Mount takes the disengage?
If a controlled mount takes the Disengage action and moves away from an enemy, does the rider still provoke an opportunity attack if he or she does not also take the Disengage action? In other words, can I ride up to an enemy, make a melee attack, then have my mount disengage and ride away, without provoking an opportunity attack?
How is a controlled Mount different from a rider?
A controlled mount has its own turn, but that turn takes place on the same initiative count as the rider’s turn. A rider and a controlled mount have separate turns, but they have the same initiative, which means you decide which one goes first. That means that, on the mount’s turn, it can take the actions that are allowed it by the rules:
How does the PHB relate to mounted combat?
The PHB describes the rules for mounted combat. In them it describes that a controlled mount has an initiative that is the same as the rider’s: The initiative of a controlled mount changes to match yours when you mount it. However, this does not mean that they act on the same turn.
What happens to the initiative of a controlled Mount?
The initiative of a controlled mount changes to match yours when you mount it. This means that on your turn you “Control” and “Release” the mount to reset its initiative. And then you let your mount act first (yielding initiative to your mount since your initiatives take place at the same time).
Can a rider be hit by an OA?
Thus, when using a mount to move around, the rider is not using their movement, action, or reaction and thus cannot provoke opportunity attacks. The only reason a rider can even ever be hit by an OA while using their mount’s movement is because the mounted combat rules specifically allow for this:
Can a horse attack on a controlled Mount?
It’s a “controlled mount”, so attacking isn’t allowed, and Trampling Charge requires the horse to make a hoof attack. You could allow your warhorse to act as an independent mount, but that has complications which I’ll discuss below. TL;DR: Move speed. What is a mount?
Can a non intelligent Mount attack while it is being ridden?
In D&D, most intelligent mounts can communicate intelligently, such as unicorns and dragons. Horses are generally regarded as non-intelligent for game purpose, or at best semi-intelligent. You can give a non-intelligent mount free rein, so that it can use whatever actions it has including attacks.
