Michael takes two attacks
Justification by rules
For this answer, I will stipulate that the following is an accurate rephrasing of Horde Breaker:
When the following conditions are met:
- It is your turn.
- You have made a weapon attack.
- You have not used Horde Breaker yet on this turn.
Then you can make another attack with the same weapon, whose target meets the following conditions:
- The target is not the target of the weapon attack that permitted you to use this feature.
- The target is within 5 feet of the target of the weapon attack that permitted you to use this feature.
- The target is within range of your weapon.
I will also stipulate that the following is an accurate rephrasing of Mounted Combatant's second bullet point:
When the following conditions are met:
- You are mounted on a creature.
- The creature you are mounted on is the target of an attack.
Then you can choose to be the target of the attack.
The sequence of events is as follows:
- Roger makes their first weapon attack, targeting Michael.
- Roger has now satisfied the requirements for Horde Breaker: it is their turn, they have made a weapon attack, and they have not used Horde Breaker yet this turn.
- Roger elects to make their Horde Breaker attack. As a first step in making this attack, they must choose a valid target. Michael's horse is a valid target for the Horde Breaker attack: is a different creature from Michael, it is within 5 feet of Michael, and it is within range of Roger's weapon. Roger chooses Michael's horse as their target, and is done with choosing the target of their attack. At this point the following are true:
- Roger chose Michael's horse as the target of their attack.
- Michael's horse is the target of Roger's attack.
- Michael now satisfies the requirements for the second bullet point of Mounted Combatant: Michael has a mount, and the mount is the target of an attack. Michael elects to use the feature, and becomes the target of Roger's attack. At this point the following are true:
- Roger chose Michael's horse as the target of their attack.
- Michael is the target of Roger's attack.
The attack is then resolved as normal, with Michael as the target.
Justification by narrative
Roger shoots an arrow at Michael. Using their skills and training, they quickly loose a second arrow at a nearby target: Michael's horse. Michael then uses their skills and training to perform a riding trick, taking the horse out of the line of fire but putting their own body at risk in the process.