Jethro Tull-"Ring Out, Solstice Bells" (from Songs From The Wood)
Jethro Tull "Another Christmas Song" (from Rock Island)
Jethro Tull "Christmas Song" (from Living In The Past, a comp that was as popular as any studio album)
Elton John-"Cold As Christmas (In The Middle Of The Year)" (from Too Low For Zero)
Emerson, Lake & Palmer-"I Believe In Father Christmas" (from Works Vol. 2)
The Who-"Christmas" (from Tommy)
Harry Nilsson-"Remember (Christmas)" (from Son Of Schmilsson)
The Band-"Christmas Must Be Tonight" (from Islands)

There must be more, this is all that popped into my head!

Argent - 'Christmas For The Free' (from In Deep)

The Ramones 'Merry Christmas (I Don't Wanna Fight Tonight)' (Brian Drain)

was the kinks' father christmas on an album besides the greatest hits?

It was on 'Misfits' but I believe it was added on as a bonus track.

The Pogues........."Fairytale of New York" is on If I Should Fall from Grace with God.

Savatage - "Christmas Eve (Sarajevo 12/24)" on Dead Winter Dead.

Christmas In New Orleans - Rickie Lee Jones from "The Other Side Of Desire"
Have Yourself A Merry Little Christmas - James Taylor from "October Road"

Christmas Song for All Year 'Round - Randy Stonehill from "Welcome to Paradise"
Christmas at Denny's - Randy Stonehill from "Return to Paradise"
Christmas with the Family - Robert Earl Keen from "Gringo Honeymoon"
River - Joni Mitchell from "Blue"

7 O'Clock News/Silent Night — Simon & Garfunkel (Parsley, Sage, Rosemary & Thyme)

Pat Benatar's 2003 album, "Go", had a hidden bonus track entitled "Christmas In America".

If River - Joni Mitchell from "Blue" counts does "She's Right on Time" from Billy Joel's Nylon Curtain also count?...

Neil Diamond: You Make It Feel Like Christmas (from Primitive)
Joan Jett: Little Drummer Boy (from first pressings of I Love Rock and Roll)
They Might Be Giants: Santa's Beard (from Lincoln)
Weird Al Yankovic: Christmas at Ground Zero (from Polka Party!)
Weird Al Yankovic: The Night Santa Went Crazy (from Bad Hair Day)
Jim Croce: It Doesn't Have To Be That Way (from Life and Times)
Angel: Winter Song (from White Hot)
Jimmy Buffett: Christmas in the Caribbean (from Boats Beaches Bars and Ballads)

Special mention: The Rolling Stones: "Cosmic Christmas" (officially untitled, the white noise tacked on at the end of Satanic Majesties is actually "We Wish You a Merry Christmas" --audible when sped up)

No, it was a non-album single in 1977.

That reminds me, that there are also greatest hits albums with Christmas songs on them that had never been on album before.

As far as I know, "Father Christmas" first appeared on Come Dancing With The Kinks 1977-1986 in 1986 (that's where I first found it).

Also, "Happy Christmas (War Is Over)" from The Alarm was a new track on the best-of Standards in 1990.

There are 2 studio albums that are Winter themed vs. full blown Christmas albums that have several Christmas songs on them.

Michael Franks - "Watching The Snow"
Kenny Loggins - "December"

John Prine -- "Christmas in Prison" (from the album Sweet Revenge)
Cracker -- "Merry Christmas Emily" (from the album Forever)
Big Star -- "Jesus Christ" (from the album Third)

Billy Joel- "She's Right On Time" (from The Nylon Curtain)
George Harrison- "Ding Dong, Ding Dong" (from Dark Horse)

Tom Lehrer---"A Christmas Carol" from Songs & More Songs

Also, If Joni Mitchell's "River" from Blue and "She's Right on Time" from Billy Joel's Nylon Curtain count wouldn't "Celebrate Me Home" from Kenny Loggins' Celebrate Me Home count?

Pretenders "2000 Miles" (from Learning To Crawl)

Same Old Lang Syne - Dan Fogelberg from "Innocent Age"

If that counts, then the John & Yoko original first appeared on album on Shaved Fish.

It's not a studio album, but Tim Minchin's "Ready For This?" contains what may be my favorite Christmas song, "White Wine In The Sun". Bastard still gets me every time.