How does a Horse with Horseshoes of a Zephyr interact with a Flying Chariot?

The new “Mythical odysseys of Theros” book contains a magic item called the Flying Chariot :

The chariot’s riders and creatures pulling the chariot gain a +1 bonus to their AC. If this magic chariot is pulled by one or more flying creatures, it too can fly.

Horses, and horse-like creatures, can benefit from Horseshoes of a Zephyr :

These iron horseshoes come in a set of four. While all four shoes are affixed to the hooves of a horse or similar creature, they allow the creature to move normally while floating 4 inches above the ground. This effect means the creature can cross or stand above nonsolid or unstable surfaces, such as water or lava. The creature leaves no tracks and ignores difficult terrain. In addition, the creature can move at normal speed for up to 12 hours a day without suffering exhaustion from a forced march.

How would a Zephyr Horseshoe Wearing Horse interact with a Flying Chariot when pulling it ?

  1. Not at all
  2. Would make the Flying Chariot float slightly above ground (4 inches) as well
  3. Would make the Flying Chariot fly