Non Christmassy Christmas Songs

For some reason there are songs which have become associated with Christmas although they actually have nothing to do with Christmas but nonetheless, you will still hear them on the radio and in department stores this December because obviously there are not enough Christmas songs so they have to include songs which happened to be released in the Festive period.
One of the best songs my ears have ever heard sung was Whitney Houston's version of I Will Always Love You which took a mediocre Dolly Parton song and sung it brilliantly but a song about loving someone which is about as Christmassy as an Easter Egg should not be in the Christmas tune rotation, no matter how well it is sung or how many chills you get on the back of your neck when she brilliantly belts out the...AND I WILL ALWAYS LOVE YOU after the quiet bit.
Another amazing song which comes under the non-Christmas song which gets played all the time once the Calendar changes to December is Keeping The Dream Alive by the German band Münchener Freiheit. Now i love this song and when the bass drum, strings and brass section kick it it really does take it up a notch but as much as i like hearing it, it is taking up valuable air-time from songs about Father Christmas and reindeer with red noses so let's keep it for the other 11 months.   
The Nat King Cole song When I Fall In Love was given the Rick Astley treatment in 1987 and by that i mean he did the reverse of what Whitney did and took a great song and made it mediocre and although it does have a video of him walking around in the snow looking depressed about not falling in love as it was an attempt for a Christmas number one, a Christmassy tune it ain't and it didn't even get to number 1 as the Pet Shop Boys deservedly beat him that year with an old Elvis song .
In the UK the version of Baby, Its Cold Outside features the Welsh duo of Tom Jones and Cerys Matthews dressed as some sorts of demons is the one you will see on the music channels but apart from
December being cold, a song about a man trying to coerce a woman into sleeping with him by plying her with drink despite her repeatedly saying no isn't really in the Christmas spirit of the season.   
I have always thought that the song Hallelujah was a great song waiting for someone great to sing it because Leonard Cohen wrote a good song and then made the mistake of singing it himself or rather talking it so the Alexandra Burke version is much better but then that is like saying the German Chancellor who took over from Hitler was an improvement. It does have the Biblical characters Samson getting his hair cut in the lyrics but otherwise a short back and sides is about as close as it gets to Christmas, which isn't close at all.
The Keane hit Somewhere Only We Know was sung by Lily Allen for the John Lewis Christmas Advert and the video had a bear being woke up from hibernation by his forest friends to celebrate Christmas which makes sense in the video and does seem kinda Christmassy but not so much on the radio or while you are perusing the vegetables in Sainsbury's.  
The film Die Hard does get mentioned as a Christmas film because on Christmas Eve Bruce Willis puts a Christmas hat on a terrorist before throwing him down a lift shaft but otherwise it is the song at the end which seems to be the decider although the lyrics to Let It Snow is about enjoying a snowy day and the coziness of being indoors, but it doesn’t mention Christmas so Die Hard not a Christmas Film and Let It Snow is not a Christmas song .
East 17's Stay Another Day is one of those songs with a Christmassy video and is a Christmas staple but in a brilliant bit of record company manipulation, a few church bells were added to the end and before you know it they had a Festive song which was written by the band's lead songwriter Tony Mortimer about the suicide of his brother.
I was going to include 'In Dulci Jubilo' and 'Gaudette' but they are apparently traditional Christmas carols from the Middle Ages so that's fair but i am going to include probably my favourite Christmas Song ever, Warm This Winter by Gabriella Cilmi.
As there is no video made for this song which is a cover of a 60's song as it was made for an Advert for the Co-Operative so it only gets played on the radio but its another song about it being cold in Winter but it does have sleighing down a mountain side and skating on a frozen lake but that's about as close as it gets to Christmas.
I am sure there are more but these are a list of the non-christmassy song to play at Christmas.