My favorite Christmas song by Elvis is Blue Christmas.
Last week, during lunch with my "Wild Lunch Bunch", we were being entertained by a singer who was obviously an Elvis wannabe. He did a good job while singing a couple of songs which had been written especially for Elvis but when he began singing Blue Christmas, I sighed and said, "Elvis OWNS that one!" One of my group took my statement literally and responded, "I didn't know he wrote it." After I explained that I thought Elvis' version was incomparable and no other entertainer could equal his version, she said that she's heard that Elvis didn't want to record it. I said, "Oh, in his 1968 TV special, he said that it was his favorite Christmas song."
Listen here to that version: