The song, Jewel in the Night, is essentially about the view of Earth from the ISS. It isn't top of our favourite Christmas tracks list, but it's sweet enough all the same.
What is particularly interesting about the song is the background noise of the fans on the ISS. Digging through Hadfield's soundcloud account, it looks like he has recorded background audio samples of the ISS. It doesn't sound quiet at all, as you might expect space to be.
Chris Hadfield is fairly prolific on the social media front for someone stuck up in space. His Twitter account features plenty of pics from the internal goings-on of the ISS and he has even done "ask me anything" sessions on Reddit.