What Christmas carol -song has initials d h f c?

The Christmas song or carol with the initials HFC is most likely "Home for Christmas", recorded by N Sync. It is the first song on the album, Home for Christmas, which was released in the US in 1998. It is the fifth song on the album, The Meaning of Christmas, released in the UK in 2002. It was written by Gary Hasse and Rozz Morehead.

Another possibility is "Hey for Christmas", or "The Shropshire Wakes" a traditional English song dating back to at least the 17th century. It was recently recorded by John Kirkpatrick, an English musician, for his 2008 album, Carolling & Crumpets.