Cinema Face said:
That war was inconclusive. Both sides think they won.
The US declared war, invaded Canada, were driven back and sued for peace. But the Treaty of Ghent didn't declare winner or loser. Because the Brits were anxious to get back to politics closer to home, they betrayed their Indian allies, ceding to the Americans lands that they had not taken, so it can certainly be argued that the US won the peace.
Certainly the Washington warmongers who promised easy victories and vast territorial conquests, then drove their new country to the brink of bankruptcy, losing every land battle but the last—fought after the peace had been settled in Europe—deserve no credit.
Perhaps the American mules in this instance were metaphorical? Like today's stubborn believers in WMDs, and easy victories.