The Seventh Day of Christmas is December 31st. The seven swans a-swimming signify the sevenfold gifts of the Holy Spirit: Prophesy, Serving, Teaching, Exhortation, Contribution, Leadership, and Mercy.
New Year's Eve was a day for games and sports. In some countries there were laws that all males of military age had to compete in archery competitions on this day, so that the king might have plenty of archers should there be a war.
December 31st is the feast day of Pope Sylvester the I who died on this day in 335.
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I do not seek to understand that I may believe, but I believe in order to understand. For this also I believe, –that unless I believed, I should not understand.-- St. Anselm of Canterbury (1033-1109)