A sleigh isn't just something Santa rides around in either.  Many people living in wintery climates might have a sleigh to get around in as well, but their sleigh would be pulled by a single horse, not eight tiny reindeer.  Hence the term, one horse open sleigh, meaning it had no roof and wasn't enclosed.  

2 hours ago, drpaladin said:

Although pronounced the same, Santa would never go on a slaying spree.

I don't know, Doc. Santa's Slay sounds like a sweet name for a metal band.

Just hear those sleigh bells jingling, ring, ting, tingling too
Come on, it's lovely weather for a sleigh ride together with you 

Bells were put on sleighs so others would know a vehicle was approaching.  In a heavy snow, visibility was limited, and since the snow muffled the sound of the horses hooves, the bells were necessary in order to avoid accidents.