Christmas card from a hooker in minneapolis - Tom Waits
There are two things that are guaranteed to make me cry. I burst out in tears every single time.
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Edward Scissorhands.
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Lonely This Christmas by MUD
“Gonna be lonely this Christmas
Without you to hold
Gonna be Lonely this Christmas
Lonely and cold
Gonna be cold so cold without you to hold
This Christmas”
How about Christmas in Prison by John Prine?
It was Christmas in prison
And the food was real good
We had turkey and pistols
Carved out of wood
And I dream of her always
Even when I don’t dream
Her name’s on my tongue
And her blood’s in my stream.
Chorus:
Wait awhile eternity
Old mother nature’s got nothing on me
Come to me
Run to me
Come to me, now
We’re rolling, my sweetheart
We’re flowing, by God…
*
etc.
Christmas Song and Another Christmas Song by Jethro Tull. The first is definitely a down song, the second kind of in the middle. Tull actually has a whole Christmas album that includes those songs and more. I haven’t heard it so don’t know how many of them are sad, but going off reputation I would guess that few of them will be that upbeat.
The lovely “December Snow” by the Moody Blues, from the album of the same name.
With October skies
You brought your love
But November came
Taking all I have and
Time, take this sadness from me
Time, bring my heart back safely
Hold on to warm September
'Cause life can be like December snow
It plays on the all-Christmas music stations on Live365.
Instantly thought of Miss You Most At Christmas Time by Mariah Carey when I saw this topic. 
Yeah, I’m a guy, and I suppose it could be considered a corny chick song, but I think she has an amazing vocal range and the song is just dripping with somber sadness. Always makes me think of some imaginary love that I’d like to be with for the holidays. Yeah, I said imaginary because all my former loves make me sick to my stomach 
… the song sort of acknowledges that in the second part, where during the warmer months you might not think much of your former love(s), but during the holidays, you wonder what it might be like if things had worked out differently and they were still around.
My kinda heartache. 
Maybe you’re thinking of “Happy Christmas (War is Over)” by John Lennon?
Lyrics here:
http://www.lyrics007.com/John%20Lennon%20Lyrics/Happy%20Christmas%20(War%20Is%20Over)%20Lyrics.html
“Please Come Home for Christmas” by Charles Brown is a good one. There several versions out there, this one is a pretty good one.
"Bells will be ringing
The glad, glad news
Oh, what a Christmas
To have the blues
My baby’s gone
I have no friends
To wish me greetings
Once again…"
I always thought that, despite the upbeat melody, that Father Christmas by the Kinks was a less-than-happy Christmas song, in both a sneeringly sardonic fashion and in a retrospective sense.
If we can consider anger as a type of sadness, I nominate “Hating You For Christmas”, the hidden track on Everclear’s So Much For The Afterglow.