I second Joy to the World and I heard a dulcimer rendition of God Rest Ye Merry, Gentlemen while I was out driving today. Actually any carol that doesn't have accidentals can be played on the HD. You may have to play it in one of the HD's native keys, but that should be no problem as long as the tune isn't too complicated for the experience level of your group.

Malcolm Dalglish does a wonderful version of The Coventry Carol on one of his albums, playing the accidental G#'s as G natural. Deck the Halls, Do You Hear What I Hear, The Friendly Beasts, Good King Wenceslas, I Saw Three Ships, Lo How a Rose E'er Blooming and What Child is This are all good choices, not too hard and decent intervals for the HD.

Have fun!