Apparently there was a severe thunderstorm and likely tornado that night - but it wasn't a hurricane as there is no record of any hurricanes in the area at all during the 1814 Atlantic hurricane season.
Whether either side thought god was 'intervening' or not doesn't mean it actually was, though. But that's too logical a thought for a tea partier.
God loves the Japanese most (completely wrecking Mongolian fleets with typhoons, twice), Americans second (protecting DC), the British third, and continental Europeans last. I base the last two on how much trouble weather over the English Channel gives Britain's enemies, for example preventing Julius Caesar's first attempt to invade Britain, and then 2000 years later providing absolutely perfect conditions for the rescue of the British soldiers stranded at Dunkirk.