Well played BH! This is my favourite Christmas Carol - according to the Oxford Book of Carols, the tune is very old indeed and versions of it are associated with various Wassailing songs. (Wassailing is an old Englishwinter or new year custom of singing to and drinking the health of your fruit trees etc in order to encourage growth and a good harvest, so that there are more apples to make into cider!)

Thank you all for the comments!

Carrie: I am sorry for the late reaction, but i hope you had good Christmas days as well!

Sam: It is one of my favorite christmas tunes. And you are right, it is played in DAC

Ron: Thank you! To try and answer your question it all depends what you think of as a Middle Eastern sound :)
Because Middle Eastern music often uses quarter notes, which are not available on the dulcimer fretboard when you want to play melody drone style.
The song i am playing in this specific video is played on a dulcimer tuned to the so called Aeolian Mode (in this case the dulcimer is tuned to DACC where the C is the melody string). This is the natural minor mode, which can give the music you play a nice and haunting sound.
On the other hand, by playing around a bit with for example in DAD (Mixolydian mode) and a capo (which gives the possibility to quickly change modes), you could figure out some Middle Eastern melodies.
I hope this kind of answers your question?

Great to hear you again Patrick! Lovely Aeolian playing.

And rest you merry too over the christmas break...

Geoff and Anne