I wish my fellows on the old calendar a joyous Christmastide. On this day after Christmas, we celebrate the Synaxis of the Theotokos. I suspect that the Solemnity of the Mother of God that the Roman Church observes on January 1 evolved from this feast. The Synaxis of the Theotokos follows a pattern in the Church calendar whereby we remember holy men and women (and angels) on the day following a great feast in which they play a part. For example, we celebrate the Nativity of the Theotokos on September 8/21 and the feast of Joachim and Anna, her parents, on September 9/22. Similarly, we observe the Synaxis of John the Baptist (January 7/20) on the day after the Theophany (January 6/19), when we celebrate the baptism of the Lord, the feast of Simeon and the Prophetess Anna (February 3/16) on the day after the Meeting of Our Lord (Candlemas on February 2/15), and the feast of the Archangel Gabriel (March 26/April 8) the day after the Annunciation (March 25/April 7).
For your pleasure, here are many Ukrainian Christmas carols: