As was mentioned, as a Ukrainian, we have a lenten meal after services on Christmas Eve. It consists of 12 dishes (for the 12 apostles). The first item to be eaten is kutya (boiled wheat with poppy seeds and honey). The wheat symbolizes immortality and hope, while the poppy seeds and honey are symbols of happiness, success and peaceful rest.
The meal is finished by drinking ozvar (fruit compote), which symbolizes sweetness of life and bounty.
Additionally, there is always an empty chair left at the table, in honor of deceased family members. It's as if they are with us at the table.
The house is still silent - no Christmas Carols, yet. There's no TV, nor radio. The joy comes tomorrow on the Nativity!
As kids our mother would stuff our stockings that hung on the mantle. Christmas morning, my sister and I would jump out of bed and run for our stockings (which we knew were filled by our mother - but, she gave credit to St. Nick for years!) The stockings would be filled with new gloves, some sparkly earrings, little toys, etc. When we went to church, we would wear the new stuff we got in the stockings - the earrings, or ring, or pin, etc. It was always fun to wear something new to church for Christmas.
Christmas day after Divine Liturgy is filled with fun! People get in groups and go caroling. Even here in the U.S. we do that. Everyone jumps in their cars and off we go to the parishioners of our church, plus local nursing homes where some of our parishioners are, etc. At each house we sing, we get fed, we chit chat and we move on to the next. Traditionally, our caroling finishes up at our priest's house. Unfortunately for him and his family, some carolers don't go home until very late at night.
We do exchange gifts, in honor of the Magi's gifts to the Christ Child. Usually this is done well into the afternoon of Christmas - after all the caroling, and eating. :-) Just some small trinket, new pj's, a book. Nothing over the top.
Mostly, it is just fun to kick back and read that new book you got, dressed in your new warm and fuzzy pj's, with the fire going, carols on the stereo, and an excuse that it is a major Holiday...and you simply cannot do a stitch of work!