She must have been crazily charming, and he must have been very drunk lol...
OMG, your character is a son of the Lusty Argonian Maid!
That's what I was thinking...
Well that's quite close to the truth
The real reason is far more complicated than that, and mostly practical in fact. Froze-His-Tail's grand grand grand father was my OB character. He was forced to flee from cyrodiil after the events there and as the master of the dark brotherhood he had enough support to flee to blackmarsh. As years past and he had kids the truth about him was beginning to reveal in blackmarsh at the same time as the dark brotherhood he was master of died out. His childs were forced to flee through Vvardenfell, now invaded by Argonians in order to survive. It was quite an adventure but when they finally got to Skyrim they settled down. Froze-His-Tail's mother thought getting nord blood into the bloodline would help her childs survive in the cold, so she used powerful illusion magic on an already drunken nord in order to do so. Her plan failed when she a few months after borth tried to see if she had managed, that's when Froze-His-Tail got his name, the obvious -Off ending to his name is something he refuses to use.
Now if Skyrim won't allow Argonians without tails... His name will be Nearly-Froze-His-Tail instead.