The white, winged stallion from Greek mythos. He does not have a horn.
It is said that upon whatever earth Pegasus beat its great hoof: a spring of purest water would burst forth; poets of old also describe him as carrying thunderbolts from Zeus.
Ultimately, Pegasus was tamed (or captured, depending on the tale) by the Greek hero Bellerophon, and used as a mount in combat against The Chimera.
Modern fiction describes pretty much every flying horse as being 'a pegasus' - as if it were the name of a species, rather than a proper-noun.