There are two fun Christmas-themed Mahjong games, both titled "Christmas Mahjong." The first game is at christmasmahjong.com and features tiles with Christmas-themed characters including Christmas trees, ornaments, Santa Claus and snowmen.
The other Christmas Mahjong game is at christmas-mahjong.com. This game has similar themes to their tiles, with brighter colors and more emphasis on ornaments, candy canes and snowflakes. It also has Christmas-themed Mahjong boards shaped like a Christmas tree, star, wreath and snowy window. Both of these games are available for free online and can be played an unlimited amount of time. Each board is slightly different than the last.