Well, I've missed our President's actual inauguration by several days, but I'd like to belatedly commemorate the occasion by offering an intriguing historical tidbit about - yes! - Jefferson's first inauguration.
The point I'd like to address (ha ha, pun alert) may seem a bit ridiculously minor to most, as indeed it did to me before I found out otherwise. But apparently the question of whether Jefferson rode a horse or walked to his inauguration has been a point of much contention over the years. The (perceived) significance of this detail lies in its potential symbolism - "republican simplicity" versus non-republican ostentation.
Not to give away the ending, but according to the preponderance of available evidence, Jefferson walked from Conrad and McMunn's boardinghouse, where he was staying, to the Capitol for his inaugural ceremony. The story that he actually rode a horse was apparently started by a British traveler who wrote later of his observance of this historic event. The part about the horse was repeated by Henry Randall (an early Jefferson biographer) and Sarah Randolph (Jefferson's great-granddaughter) in her Domestic Life of Thomas Jefferson.
To make a long blog entry shorter, I'll just say that there doesn't seem to be any good reason to believe that Jefferson rode a horse to his first inauguration. There is a pretty sharp-tongued and thorough drubbing of the horse story in the February 1888 issue of Harper's Monthly Magazine (which you can all read in the comfort of your homes thanks to the good offices of Cornell University - see page 473).
Also, a special random inaugural-themed bonus - much of course has been made over the various books that Presidents and other politicians use or don't use to be sworn in with. Here's a handy list, should you find yourself needing it, of what every president since Washington has been sworn in with, compiled by people at the Office of the Curator at the Capitol.