A quick Google search comes up with several sites that say "Little Christmas" is another name for Epiphany, or Twelfth Night, on 6th January. It is celebrated by a number of different cultures around the world, sometimes as "Women's Little Christmas" (presumably because it was a well deserved rest after the busy holiday period).

..... but I suspect that Steve is right - that "little" was the only word the songwriter could think of to make that line fit his tune

DC