William Henry Harrison set a record for being the oldest president at the time of his first inauguration. His age was 68, when he was inaugurated on March 4, 1841. That record held for 140 years, before it was broken by the 69-year-old Ronald Reagan in 1981.
Many of the early inaugurations were held indoors, in either the House or Senate chamber. But, by 1841, the custom of having the event outdoors on the Capitol grounds had taken hold.
Accounts of Harrison's inauguration differ on some details. However, two things seem certain: 1) the day was wet and cold, and 2) his inaugural address was the longest in history. Various sources have it anywhere from 1 3/4 hours to more than two hours.
The big question is: Did Harrison's fatal illness result from exposure to the elements on his inauguration day? He died of pneumonia after one month in office.
His Wikipedia entry, as currently written, argues that his symptoms first appeared more than three weeks later, so it seems doubtful that he contracted the disease on March 4. Other accounts, such as this one, support the traditional story that he did contract the disease on the day he was sworn into office.
The tale of the fatal inaugural address makes for good storytelling. But we'll probably never know for sure.