
reefwood |
Would a Nightmare Skeleton retain the extra fire damage of its hooves?
Nightmare
Melee bite +9 (1d4+4), 2 hooves +4 (1d6+2 plus 1d4 fire)
Skeleton
Special Qualities: A skeleton loses most special qualities of the base creature. It retains any extraordinary special qualities that improve its melee or ranged attacks.
Is the extra fire damage a supernatural or extraordinary quality?
The "Burn" quality is extraordinary, but the Nightmare fire damage isn't exactly that. If it was, it would be listed as "Burn" and this would also mean that it could catch you on fire.
My guess is that since the Nightmare flies by magic means, then the fire damage is also magic, which would mean supernatural. And I'm guess this would mean that the fire damage is lost when it is turned into a skeleton.

reefwood |
I would say that strictly using the template it would loose flight and fire to attacks. But then, it just isn't as cool. So I would allow it to keep both flight and fire to attacks. Just because that is way cooler.
I don't have any question about the flight. That seems to be correct according to the template (which loses flight from wings but retains magical flight).
How was the Nightmare Skeleton Made. Being an Outsider a normal spell will not let them do that. It also says that they lose all their special abilities when it is made to be a Skeleton.
It was made with the animate dead spell. I'm know there are restrictions to restoring life to an outsider that is outside its native plane, but I don't see any restrictions about other spells or anything to do with necromancy.

Pale |

How was the Nightmare Skeleton Made. Being an Outsider a normal spell will not let them do that. It also says that they lose all their special abilities when it is made to be a Skeleton.
Spells that restore the soul to the body don't work on outsiders. Animate dead doesn't do that so it works no problem.
I would rule that it's a flying (wingless) horse skeleton with flaming hooves (mane and tail, too) that do no extra fire damage because, hey, it's a cool image.
You could also make it a burning skeleton. I would personally allow the nightmare to keep its smoke ability and ditch the fiery death explosion effect for that.