The Christmas season goes past Christmas and really ends with the feast of the Epiphany. This occurs on January 6. The day is celebrated as the day the three wise men arrived to visit Jesus, bringing gifts with them.
It is unlikely a visit could have occurred in just under two weeks. Organization of a trip in the days before telephone would have meant sending word physically. And the caravan would have traveled slowly, once organized. A couple of years would be a better estimate of the time needed. Yet a twelve-day celebration is acceptable, for a two-year celebration would overlap other Christmas Days.
January 6 ends Christmas time for many, albeit not all. In some cultures, the twelve days of Christmas are a time for continued gift-giving. As an example, consider the Christmas booths that sell items for giving in Rome. They will stay until the last gifts have been bought.