Christmas, in the modern sense, is a holiday paradoxically a day long that stretches into the month-and-a-half period preceding Dec. 25. It grinds to a halt on Dec. 26.
In olden times, Christmas wasn't so much a "season" -- it was a 12-day-long celebration, just like in the song. And it began on Dec. 25 instead of ending there.
Thus Wednesday is still Christmas -- in fact, it's only the third day of 12.
According to an article in Christianity Today, the days following Christmas day are traditionally feast days. Dec. 27 is the feast of St. John the Evangelist. This is followed on Dec. 28 with the feast of the Holy Innocents, commemorating the children killed by the order of King Herod.
What we know as New Year's Day is, perhaps surprisingly, a feast day to celebrate Jesus' circumcision.
Many of the traditions of the 12 Days of Christmas (like those in the single-day version) predate the notion of Christmas, and are rather holdovers from older wintertime celebrations, like the Roman holiday of Saturnalia.
One of these very old traditions, still celebrated in some Hispanic communities, occurs on Epiphany, the end of the 12 nights. In Spanish it's called "Día de los reyes magos" (Day of the Three Wise Men or Day of the Magi), and often involves hiding a small figurine of Jesus in a cake. Whichever family member finds the figurine is in charge of fun and merrymaking -- a tradition known in English as the "Lord of Misrule."
The same practice existed in Saturnalia.
In the United States, the significance and celebrations of the Twelve Days of Christmas have long been forgotten, replaced over a century ago by a calendar dominated by early Christmas buying.
But in the spirit of the Twelve Nights of Christmas, it may be best to reserve judgement of those who leave their Christmas decorations out well past Christmas. It's not over until Jan. 7.