Like all horses it wasn't very bright. Perhaps not smart enough to realize that it simply must have weighed too much to be able to fly. Then again, maybe it possessed some mysterious buoyancy mechanism. As of yet we have not acquired a live or fossilized specimen for study. No real reason to kill these, but if you wanted to a gun would probably do the trick.
Unicorns are a whole different ballgame.
In fact, they may be some kind of woodland spirit that merely takes the form of a horned white horse. Furthermore, this horn is only visible to a pure maiden. Our theory is that unicorns may be as abundant as ever, just that the number of pure maidens has declined precipitously. We don't really know what that means but we imagine that our clearcutting, uranium dumping and mutant deer hunting probably qualify. We aren't exactly sure what harm a smart horse with a horn could do to our sport utility vehicle, but imagine that a hand grenade should prevent the issue from ever arising.