After a solid hour and a half or so of pure destruction on Game of Thrones, we need a breather from the madness of the penultimate episode. Perhaps the writers felt the same, because after that brutal sack on King's Landing, we got a lengthy quiet scene. Arya, who gets sidetracked from killing Cersei, manages to survive all the destruction and meets up with a blood-spattered white horse . . . who also manages to avoid all the destruction. She slowly makes her way toward it while nothing but burnt corpses and rubble surround them, and then she rides off. What?
First of all, Arya's lucky to be alive considering the shape the city's in. Though she and The Hound made a beeline for the Red Keep, he tells her to get out when Daenerys begins burning the place down and won't stop. Arya runs and stumbles through King's Landing, getting injured and attempting to save people along the way. At the end of it all, after she's escaped from the debris of a building that collapses around her, she comes face to face with that white horse. It's an effective way to illustrate how much damage Dany has done to King's Landing and how many people are killed.
Of course, it's significant that she runs into a white horse and not, say, Jon or some other human. The obvious and quite on-the-nose answer may that Arya is, and has been, a symbol of death. Her whole character arc has revolved around death — she's already killed many on her list and ultimately killed what was thought to be the biggest threat to Westeros. This white horse could be a nod to the Christian concept of the Four Horsemen of the Apocalypse (aka four guys on horses who bring about the apocalypse). Though instead of representing death, this would mean Arya represents Christ. Perhaps Arya is no longer a harbinger of doom, and is functioning as the savior to Westeros. If this is true, it makes sense that the scene comes after her life-changing discussion with The Hound.
There's also an interesting connection with Dany and white horses, too. In the first season, Dany receives a white horse from Drogo as a gift. It dies in season two while they're riding through a desert and lacking water, and Dany is particularly upset because the horse was her first gift from Drogo. This brings us back to Arya as a symbol of death, and could potentially foreshadow bad news for Dany.
Other theories: The horse could be The Hound, reincarnated to help Arya achieve her destiny. The horse could be symbolic of Arya's tainted childhood, at first pure and undisturbed, then violently ripped away with bloodshed. Finally, the horse may just symbolise hope for the future — both as it pertains to Arya and Westeros.
Of course, there have been lots of white horses on Game of Thrones, so any perceived symbolism and callbacks may be a coincidence. One thing is for sure though: Arya's riding off to wherever she's going with a purpose. We'll just have to wait until the finale to see what it is.