1. Something—especially an issue or topic—that is no longer of any use or relevance (as used in the phrase "beat/flog a dead horse"). The President's pledge to overhaul the education system became something of a dead horse after the economy crashed. We've all moved on from that problem, so there's no use beating a dead horse.
2. (dated) A seaman who incurs debt for wages paid in advance. Countless men became dead horses on their ships, trapped paying off debts that were in themselves incurred to pay off other debts, in an endless cycle.