Pegasus doesn't have a horn. It's a mythological creature commonly depicted as a divine white horse with wings.
What we found is the Unicorn whose name is derived from the Latin for ‘one’ and ‘horn’. While the most popular image of the unicorn is one of a horse with a horn on the forehead, early depictions of the unicorn described a horse like creature with a beard like a billy goat, the tail of a lion, and cloven hooves.
According to popular culture, the Pegasus was supposedly the creation of the ancient Hittite god of thunderstorms, Pihassassa. Numerous other stories have been ascribed to its origins as well, with many mentioning it as a winged stallion with a brother named Chrysaor. These creatures were supposedly from the springs of Oceanus, which was located at the edge of Earth.
Learn more about the creatures and monsters from Greek Mythology at Greekgodsandgoddesses.net.