Maybe this is too far fetched, but this is a theory that I have come up with my friend Sarang. Please don't find this offensive or blasphemous etc.
Imagine a Sardarji in his 60s with grey beard and with Red Turban (pagdi) who is amongst the first western immigrant. Now consider his name as Santha Singh Kailash. He is not that well educated and because of his desi accent he gets the name 'Santa Claus'. He also tried to communicate in his Hinglish accent about "Jungle Bail" (Bail is indian buffalo which is used for ploughing in the farms) and how is "cart" was driven by the "bail". Since there were no buffalo's in the cold western world it was approximated to rein deer. Over the ages the story took the form on Santha Kailas aka Santa Claus driving the cart pulled by rein deers and singing Jingle bell. Also the indian buffalos have bells attached to thier neck, so there may be some connection there. I would leave it upto your immagination as to how "chimney" etc came up in this story.