I wish every day could be like Christmas (1992 bside keep the faith)
Please come home for Christmas (1994)

As far as I know they are the only ones which have been recorded officially as a band.

Live they and Jon solo have done both of the above and:

Run Rudolf Run
Back door santa
Blue Christmas
(Christmas baby) Please come home(not to be confused with PCHFC) - This was Jon solo at a benefit concert - my personal fave xmas cover.

Other members will be able to fill you in with more details