Reagan's was
held privately on January 20, 1985 and publicly on January 21, 1985, the day before my daughter was born.
As January 20 was a Sunday, the swearing in of Ronald Reagan took place privately in the Grand Foyer of the White House, although it was televised. The following day, January 21, Chief Justice Warren E. Burger administered the oath publicly at the 1985 inauguration. As the weather outside was harsh, with temperatures near zero degrees Fahrenheit, the planners were forced to cancel most of the outdoor events, and the inaugural address was delivered in the Capitol Rotunda.
http://en.wikipedia.org/wiki/Second_inauguration_of_Ronald_Reagan
Those chickens! Was too cold for them BUT I WALKED from Metro to my DC apartment (and gave birth the next day!!!)