Yes, you can use horde breaker with the Attack granted by haste
Horde Breaker says:
Once on each of your turns when you make a weapon attack, you can make another attack with the same weapon against a different creature...
Since haste grants the ability to make one weapon attack as part of an Attack action, it will definitely be a valid trigger for the Horde
This will work even though haste specifies that the Attack action can be used to take only one weapon attack, because the Horde Breaker attack is not made as part of that Attack action. It just happens to be triggered by that action, so it does not violate that stipulation.
So, because the haste attack is a weapon attack, you can use Horde Breaker to make an additional attack.
A couple things to note though:
- Horde Breaker can only be used once per turn no matter what features you use to trigger it.
- This means that if you take the Attack action normally and make an attack, then use haste to take the Attack action again and make another attack, you cannot get an additional Horde Breaker attack with both attacks - only one (per turn).
- The horde breaker attack must use the same weapon and target a different creature within 5 feet of the original target.