First off here is O' Tannenbaum.
Ernst Anschütz, a organist from Leipzig wrote the modern song we know in 1824. He based it on a 16th century folk song. It wasn't intended as a Christmas song but gained popularity as such in the early 20th century (info from wikipedia).
O'Tannenbaum sung by Nana Mouskouri
Next is Stille Nacht, Heilige Nacht, probably one of the most Famous Christmas songs of all. The music was scored by Franz Xaver Gruber and the lyrics were written by Joseph Mohr in Oberndorf bei Salzburg, Austria in 1818. Appropriately sung here by the Vienna Boys Choir.
Those were the only Christmas song that I know to be originally writen auf Deutsch. I wasn't happy with just these two so I did some searching and found a few Christmas Songs from Rolf Zuckowski.
Rolf Zuckowski a German Musician and Music producer from Hamburg. He is known for haveing written many song for kids and has a whole bunch of Christmas songs too. He seems to be German equivalent of Raffi. Raffi is a US Americans song writer, he wrote hits in the 80's like "Baby Balooga in the Deep Blue Sea. . ." and also has a Great Christmas Album. Which I still listen to each Christmas.
Well, most kid songs I can't get into these days, specially German kid songs. Though luckly I found one that is not bad. Lasst Uns Froh und Munter Sein (Lets be Happy and Jolly) by Rolf Zuckowski.
Have a Merry Christmas!!