The stuff I end up spouting off... Victory Star ♦♦♦ made a post about linking ponies with Greek gods... So I ended up writing a wall of text on Pegasus & Rainbow Dash.

If we're going Greek... We have a horse god here.

Pegasus is Chrysaor's brother. It's a weird version of the 'Horse Twins' myth like the Indic Asvins and the (also) Greek Dioscuri (Castor & Pollux). In this variant though instead of two horsemen, one who is mortal and one who is immortal, what resulted from Poseidon and Medusa was a mortal human and his brother... an immortal horse god. Later myths paired him with Perseus and Heracles because flying around on a divine winged horse is the pimpin-est ride yo.

If anyone owns him it's Zeus who made him the bearer of his Thunderbolts and some weather functions (this probably happened due to his link with a Luwian weather god named pihassas who is ether his origin or a deity who was fused with him later in lore and the fact that the rising of his constellation marked the beginning of Spring and the start of the seasonal rainstorms in Greece - Winter Wrap-up! tongue ). His other side is that he is the horse of the muses and there are several springs Hippocrene sacred to Pegasus & the Muses in Greece where he stuck the ground with his hooves and the waters of inspiration burst forth from the ground.

If Pegasus had a pony it would have to be Rainbow Dash - because let's face it she's Pegasus' own Pegasus: Head of the Ponyville Weather Patrol, Inspired the rest of the mane six to get their cutie marks with her bursting Sonic Rainboom, her emphasis on action, her heroics, et cetera.

Also nit-picky but you're thinking Helios whom Apollo was connected with... The appropate deity connections would be:
Helios & Selene (Greek) or Sol & Luna (Roman).

Interesting enough in the story book that came with the molded toys Princess Luna is called Princess Selena.