I went through this with my husband a couple of yars ago when I was painting a mural at an Italian restaurant and listening to their Christmas CD’s all day every day… they had three different versions of “A Visit from St. Nicholas” (one was read by Louis Armstrong, which was really something to hear). After a while I noticed that some of them said Donner and some of them used Donder, so we went on a research mission to find out which one it was really supposed to be.
Personally I like Donner better–isn’t that what they used in the Rudolph special? I do think it’s weird that he would use one German word and one Dutch word, rather than keeping them both the same.
I believe Burns was the first to write it down. I think there is some question as to whether he wrote it or just copied down song lyrics he heard from someone else. IIRC, Burns did not claim it as original, but some believe Burns did write it himself, his protestations to the contrary notwithstanding.
That’s all from memory. I’m sure someone will come in and straighten out any errors in my explanation.
New literary scholarship suggests that Clement Moore did not really write A Visit From St. Nicholas, but that it was written by a guy named Livingston, of Dutch descent, thus explaining the original reindeer names. See also this thread where the internal link to another article on the same topic no longer works.