This excerpt from my Introduction to Folklore may help:

The modern celebration of Christmas draws on two European traditions, the pre-Christian, Germanic death festival and the Roman Saturnalia. For the Romans, the shortest days of the year were made even more sacred as the time of the birth of Mithra, a semi-divine figure in a popular mystery cult. Mithra was the son of heaven who descended into the depths of hell to defeat the author of evil in the world. Romans celebrated Mithra’s birthday on December 25. The Empire imported and modified the worship of Mithra from the east, where it originated in modern-day Iran. Mithraism, with its strong strain of Stoicism and duty, was especially popular in the Roman army.

In 354, the pope declared December 25 as the birthday of Jesus. It was an attempt to incorporate an important holiday and to obscure the worship of a pre-Christian god. When this tradition came north, either in its pre-Christian or Christian form, it met the Germanic death festival. This was a time when the souls of the dead could come back and visit the living, and it was an opportunity to foresee how life would be in the following year. The ancient idea that Yule is the time for predicting the future is behind the notion of the song “The Twelve Days of Christmas.” Modern Americans often misunderstand the twelve days of Christmas, frequently regarding them as the last shopping days before the holiday. In fact, they are the days that begin with Christmas and end on January 6, Epiphany. According to tradition, this was the period that spanned the birth of Jesus and the adoration of the Magi. In America, the twelve days have shifted from a time of celebration to one of preparation. Christmas Day serves as the climax rather than the beginning. Even the wise men now appear on Christmas Eve in most American traditions.

The song “The Twelve Days of Christmas” has meaning now lost to most people. For example, the number of gifts the song describes is no accident. There is, of course, only one gift – the partridge in a pear tree – on the first day, but as anyone knows who has sung the song, the number of gifts quickly escalates. Thus, there are three gifts on the second day – two turtledoves and yet another partridge. There are six gifts on the third day and so forth until seventy-eight gifts appear on the twelfth day. The gifts from all the days total 364, one for each day of the year (minus one).

This is more than a clever trick placed subtly in the carol. European folk culture traditionally viewed the twelve days of Christmas as the time when one could predict the future. Each day represents one of the months of the coming year. By watching the weather or performing magic on any given day, one was able to forecast the nature of the corresponding month in the following year. The number of gifts in “The Twelve Days of Christmas” apparently draws on the belief that the Christmas season magically reflects the following year.

Yet another tradition surrounding this carol is the role it once occupied as a game. As an Irish farmer from County Clare told a folktale collector in 1940, one child hands another a bucket of turf asking “What’s that?” The recipient then answers, “Two ducks and a fat hen,” passing it back with the same question, which is answered with an additional three items. The first one to fail reciting the items in order loses. This sort of game appears to be behind the carol “The Twelve Days of Christmas,” which retains a humorous quality.

More importantly, however, the song reflects the predictive potential of the season. It was easy for European peasants to assume that the end of one year was a good time to look into the next. By sitting at the crossroads on the night before Christmas and not talking or eating, Icelanders believed that visions of the future would appear.

Many Northern Europeans maintained that a young girl could use magic on Christmas Eve to divine the features of her future husband. With a lighted candle in hand, she could look into the Christmas beer and see his face. By pouring molten lead into water and examining its form, she could predict his occupation – a nail for a carpenter, a horseshoe for a blacksmith, etc.

That would be a great question for a separate post to attract Roman history experts (of which I am not one!).