I knew there was a white stallion associated with rising the sun somewhere in Indic lore! Finally managed to track him down (despite the fact that he's been more or less staring me in the face for a while now):

It's Hayagriva and his Vedic prototype Dadhikrāvan!

Sridhara Babu - Hayagriva. The Horse-Headed Deity in Indian Culture

One of the several hymns dedicated to the cosmic stallion Dadhikrāvan who ushers in the morning:

Rig Veda Hymn 4:39 Dadhikrās. (Griffith Translation)

1. Now give we praise to Dadhikrās the rapid, and mention in our laud the Earth and Heaven.
May the Dawns flushing move me to exertion, and bear me safely over every trouble.
2 I praise the mighty Steed who fills my spirit, the Stallion Dadhikrāvan rich in bounties,
Whom, swift of foot and shining bright as Agni, ye, Varuṇa and Mitra, gave to Pūrus.
3 Him who hath honoured, when the flame is kindled at break of dawn, the Courser Dadhikrāvan,
Him, of one mind with Varuṇa and Mitra may Aditi make free from all transgression.
4 When we remember mighty Dadhikrāvan our food and strength, then the blest name of Maruts,
Varuṇa, Mitra, we invoke for welfare, and Agni, and the thunder-wielding Indra.
5 Both sides invoke him as they call on Indra when they stir forth and turn to sacrificing.
To us have Varuṇa and Mitra granted the Courser Dadhikrās, a guide for mortals.
6 So have I glorified with praise strong Dadhikrāvan, conquering Steed.
Sweet may he make our mouths; may he prolong the days we have to live.
Source: http://www.sacred-texts.com/hin/rigveda/rv04039.htm

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.