The Nightmare's Lore entry describes the creation of the monster:
Nightmares don't appear naturally in the multiverse. They must be created from pegasi. The ritual that creates a nightmare requires the torturous removal of a pegasus's wings, driving that noble creature to evil as it is transformed by dark magic
The Nightmare does not have wings any more, but it still has a fly speed of 90 feet, matching the Pegasus it once was. It has been created by dark magic. Does the flight count as magical for rules purposes like the falling rules?