Doh, I should have read the whole Wiki page. Harrison was inaugurated in March, not January but I think my point (kind of) still stands with this:
"When Harrison came to Washington, he wanted to show that he was still the steadfast hero of Tippecanoe and that he was a better educated and more thoughtful man than the backwoods caricature portrayed in the campaign. He took the oath of office on Thursday, March 4, 1841, a cold and wet day.[102] He braved the cold weather and chose not to wear an overcoat or a hat, rode on horseback to the ceremony rather than in the closed carriage that had been offered him, and delivered the longest inaugural address in American history[102] at 8,445 words. It took him nearly two hours to read, although his friend and fellow Whig Daniel Webster had edited it for length. He rode through the streets in the inaugural parade[103] and attended three inaugural balls that evening,[104] including one at Carusi's Saloon entitled the "Tippecanoe" ball with 1,000 guests who had paid $10 per person (equal to $297 in 2020).[105]"