No matter how much pop elements you have in a song - computerized drums, generic beats, guitars and PROCESSING, you cannot have a Christmas song without the bells. A Christmas song without bells is like an acoustic-y song without a guitar part - wherever you are in the world, it just doesn't happen and no one over thinks of a song without it. Bells are one of the main reasons why Christmas songs are Christmas songs! Heck, you can put some bells into any random song and it would most probably sound a little like the season.
Here's exactly how you turn a song Christmas-y by simply adding bells. The chords and melody are identical and the arrangement is pretty much the same - the only different are the lyrics and the fact that one is for Christmas and one isn't but they're not basic musical elements so yeah.
The bells are heard the most during the chorus of the 2nd song and that's the main, MAIN thing that actually makes it Christmas-y.
The original song
(not very Christmas-y but I don't know why one of the dancers has a Santa hat on. Whatever - it sounds less Christmas-y than the second video):
The Christmas-ized song: