Pegasus is associated with the Muses. With a kick of his hoof, Pegasus created a spring on Mt. Helicon that is called Hippocrene and offers inspiration.
Pegasus is also sometimes considered one of the constellations.
The Greek hero Bellerophon tamed and rode Pegasus using Athena's magical golden bridle. After Bellerophon foolishly tried to use Pegasus to reach Mt. Olympus, the immortal rider-free horse Pegasus went to Mount Olympus bringing thunder and lightning to Zeus.
More sources: "The Son of Neptune," by Arthur Stanley Pease. Harvard Studies in Classical Philology, Vol. 54, (1943), p. 82.