This song is biblical, but in a non-religious creative sense. Someone earlier mentioned dystopia, and yes, to a point you're correct. This song is about the obliteration of "sin" in Sodom and Gomorrah. First, Dog Days in ancient Egypt, were considered cursed, and also periods of ritualistic sacrifice to the "gods" to appease natural disaster. With this, Sodom and Gomorrah were noted in the Bible for significant sexual deviance and more notably, Idol worship. God tells Lot, before the destruction of the city, "I'm going to allow you and your family safe passage, because this place is going down. DO NOT look back, and don't doubt that you'll be punished if you do." The "Her" is Lot's wife, who very much loved her city. As they flee, she looks back with longing on a place she didn't want to leave, because she loved it too much. God kept his promise and transformed her in to a pillar of salt.
The horses represent the Bible, and it's promise that God would send horses as a sign of warning to the end of days-Riders would lead these horses in and Hell would follow them over earth.
Songwriters use Biblical reference, obscure or otherwise, to create great music. The Killers also did this with one of their most famous songs, U2 as well. It makes for some good writing, ironically.