For this page, there are several actions to consider:
One option is that, if you believe that Christmas should be a day of reverence, is to choose a day close to December 25 to have the gift exchange. In this way, Christianity is not a faith of deprivation.
In fact, in some areas of Latin America and Spain, people celebrate Three Kings Day as the day to exchange gifts, usually 12 days later, on January 6. This is celebrated as the day that the wise men visited Jesus, even though Scripture never states how many wise men there were.
Another action is to remember the limitations of the Christmas story. Nowhere does Scripture state how many wise men there were, nor does it state when the wise men showed up (probably roughly 18 months after Jesus' birth).