In Poland, Christmas Eve is the main gift giving day and is celebrated with at least twelves dishes with an extra plate for unexpected guests. It is said on this magical night, animals can speak like humans. Hopefully, no one runs into a goose which is their main Christmas dish. Meanwhile, in Germany children see the Chritsmas tree for the first time on December 24th and spend the night decorating it.
In addition to exchanging presents on different days, countries also have different traditions. For example, in Spain, the centerpiece of the house is the Nativity scene, not the Christmas tree. In the Catalunya region, if you find the figurine of caganer (the crapper) among the donkeys, wise men, Joseph and Mary, you're supposed to have good luck the following year, while presents are delivered by a crapping log called the cagatió. You can read more about it here.
Any other traditions you can think of?
Have a safe and enjoyable holiday season however you celebrate it!