Despite claims of many different holidays and observances on January 3, the only one that I found to have much significance is the 10th day of Christmas–which according to the song is 10 lords a-leaping. Not terribly exciting, but for this time of year, I can understand being a little tired a couple of days after the new year revelries.
Speaking of lords a-leaping, the most famous one to come to mind is Mikhail Baryshnikov, who was born January 27, 1948. Read more about him here.