Snorri also lists the other ten horses belonging to the Twelve** Aesir in the Prose Edda: Glad (Joyous), Gyllir (Golden), Glær (Shining), Skeidbrimir (Swift-Going), Silfrtopp (Silver-topped), Sinir (Sinewy), Gisl (possibly "Gleaming"), Falhofnir (Hollow-Hoofed), Gulltopp (Gold-topped) and Lettfeti (Light-Feet).
There are also Skinfaxi and Hrimfaxi, the horses which bring daylight and night, respectively. Skinfaxi posesses a brightly burning mane*** and Hrimfaxi sprinkles the ground with his spit and foam as he runs through the sky, which explains the source of dewdrops quite neatly.
Then there are Arvak and Alsvinn (not to be confused with Skinfaxi), who draw the chariot of the sun which is driven by Sol. These two also seem to be outfitted with an early air conditioning system -- bellows strapped beneath their shoulders to keep them cool (they are pulling the SUN, after all).
That Thor does not seem to have a horse is pretty telling, and makes sense in context with his position as god of the common man, in contrast with Odin, who is quite clearly a god of Noblemen and kings with his horse which is not only completely unique, but the best of the best. In fact, not only can Sleipnir travel to Hel and back, but Odin wagered his own head on Sleipnir's speed and raced him against the giant Hrungnir's horse, Gullfaxi (Golden-mane). Even when Thor wins Hrungnir's horse later (by dueling with the giant), he ends up giving Gullfaxi away (to his son, Magni), rather than keeping it for himself.
In the Skírnismál, Freyr also has a pretty fancy (but unnamed) horse** which is described in the eighth stanza of the poem:
"Then give me the horse | that goes through the darkAnd Freyja has a horse named Hofvarpnir****, which she rides on Frigg's business to the other worlds, and is capable of galloping across the sky and the sea.
And magic flickering flames;"
By no means should this be considered a complete list of horses, but the last one I'm aware of with any association to the DIVINE is Grani, a descendent of Sleipnir, and Sigurd's horse in the Saga of the Volsungs. Grani, as it happens, is also gray, just like his forefather, and he's described in the saga as "the best horse there ever was." Barring Sleipnir, of course, I'm sure.
*A man and his stallion were contracted to rebuild the wall around Asgard, and if he finished in a certain period of time, he was to be paid with the sun, the moon, and Freyja. When it looked like this guy was going to finish in time, Loki transformed himself into a mare in order to lure the stallion away, so his owner could not complete the wall. The gods only made the deal because Loki convinced them it would be impossible for the man to complete the task. But it turned out (of course) that the man was a giant, so after they cheated him, and he revealed his giant-nature, the gods just went ahead and let Thor kill him. Loki disappeared for a while after that, only to return with Sleipnir trotting at his heels.
**Snorri tells us that Thor himself, walks, but remember that Snorri's Twelve Aesir is actually Fourteen Aesir, so it makes me wonder who else catches a different ride to the root of Yggdrasil where they all meet up -- If Balder is dead, that would mean only one other person is left without transportation, but if he isn't, since Freyr gives up his sword in order to win Gerd as his wife, maybe he gave her his fancy-magic horse, too, while he was at it. In any event, the meanings of the horses' names came from the Grímnismál.
***Skinfaxi translates literally as "Shining-Mane" which I guess makes Hrimfaxi Frost-Mane or Foaming-Mane, which makes a certain amount of sense considering night is generally colder than day.
****Hofvarpnir's parents are Hamskerpir and Gardrofa.