When I was growing up, we celebrated Christmas on December 24 and "Old Christmas" on January 6. I was taught that this was the "true Christmas" because this was the day Christmas fell on before the calendar was changed. I never really knew what that meant, "when the calendar was changed." I now know that this was a reference to the Julian calendar being changed to the Gregorian calendar in 1582. Apparently not everyone adopted this calendar right away, but eventually most did for the sake of international trade. Greece was the last European country to adopt the reformed calendar in 1923. (This information is directly from Wikipedia).
We celebrated one Christmas with Mem's side of the family, and one with Datt' side. At least until Datt's family moved to Cashton, Wisconsin. It always felt like we celebrated with the rest of the world in December, and then the Amish observed their own private Christmas in Janauary.
We were not allowed to work on Old Christmas. We observed it as a religious holiday, just as we did Christmas and as we observed the Sabbath on Sundays. I don't know whether the Amish today still observe this day as holy. I can imagine that as more Amish people work at factories, this could become more difficult to do, since employers don't want the Amish portion of their work force to be missing that day.
In my research about Pennsylvania Germans, I found that the Amish were not the only ones who observed this holiday in colonial Pennsylvania. The "church Germans" (Lutherans, Reformed, and Calvinists) along with the sect Germans (Mennonites, Amish, Schwenkfelders, and Moravians) all observed Old Christmas. In fact, it was the Germans who successfully pushed for Christmas becoming a national holiday in the U.S. Congress after they said they wouldn't be showing up on that day. It was decided that legislation could not proceed without their presence. Steven Nolt's book Foreigners in their own Land: Pennsylvania Germans in the Early Republic is a great read about how German traditions survived for many generations. It seems to me that the Old Order Amish and the Old Order Mennonites are alone in carrying on these traditions.
I hope you have enjoyed Epiphany or Old Christmas, or whatever January 6 means to you. I also hope you will be showered with Blessings along the roads you travel in this New Year.