The horse's heads symbolize the fate of the speaker, who is being driven inextricabably to eternity. The reference evokes the biblical symbol of the "Four Horsemen of the Apocolypse," in which the horses represent the last physical state of being: one's final consciousness of life before the abyss of death (the absence of consciousness).
Here is the whole stanza, which concludes the poem:
Since then -- tis centuries -- and yet / Feels shorter than the day / I first surmised the Horses Heads / Were heading toward Eternity --
As you can see, from her new state of being, the speaker references her last moment of consciousness in this life, when she realizes that her days on Earth are about to end and her new existence is in "Eternity" has begun. The speaker is contemplating just how long it has been when she first observed the grave, "A swelling of the ground." The Horses were the vehicle in which she was transported from the old life to the new.
“Since then—’tis Centuries—and yet/ Feels shorter than the Day/ I first surmised the Horses Heads/ Were toward Eternity.”
As Emily Dickinson was a very religious young woman, it may be safe to conclude that the horses represent the horsemen in Revelation who not only represent eternity, but also the means in which death will come to those on earth after the rapture.
However, it is more likely that the horses are just the vehicle in which the passenger is transported by her chaperone to the next world...something non-threatening which all would be familiar with and would not draw undue attention from nosy neighbors peeking out their windows.
the Horse's Heads symbolize two knights. A dark knight (the prince of the power of the air) and a White Knight - the Lord Jesus Christ