A little comment about the horses:

I thought the poem invoked the medieval and early modern practice of "quartering", when an individual was tied up to four horses running in opposite directions and tearing the body up (Foucault uses this a lot in his writing and the other discussion on the Ayal reminded me of this). In this respect, it is the living flesh of the relationship (described so well in the second verse) whch is torn by the individual horses running in separate directions.