The real origin of the holiday classic 'Jingle Bells'

Claims that Jingle Bells started as a Thanksgiving song are making the rounds online again. So, how did the holiday classic actually come to life?
NPR

A look at the history of jingle bells

UNIDENTIFIED CHORUS: (Singing) J-I-N-G-L-E bells. SIMON: Ah, jingle bells. Don't worry. Not going to sing along, but I would like to pose a question. How did those bells become a symbol of this season ...