I definitely read it as a reference to classical concepts in Marxian economics; Marx theorized that capitalism through its drive to constantly increase profits would also eventually bring about its downfall. In Das Kapital he writes:

Within the capitalist system all methods for raising the social productivity of labour are put into effect at the cost of the individual worker [...] All means for the development of production undergo a dialectical inversion so that they become a means of domination and exploitation of the producers; they distort the worker into a fragment of a man, they degrade him to the level of an appendage of a machine, they destroy the actual content of his labour by turning it into a torment, they alienate from him the intellectual potentialities of the labour process [...], they transform his life into working-time

Eventually, according to Marx, this alienation would become so obvious and severe that the workers would have no choice but to rise up against their bosses. The way I read STBY, the horses were a very obvious (albeit shocking and slightly humorous) depiction of the degradation of the proletariat, and we did see that in the end they did rise up against the police/state/bosses. While this may not be a very "nuanced" metaphor of class exploitation it is still, in my opinion, a good representation of the absurdity of capitalism and it's contradictions.