I haven't seen the film, but here's a list of what's on the soundtrack. You might be able to identify the hymn you're looking for from it.

Regards
Marion


Cold Mountain (Music From The Miramax Motion Picture)" Track Listing:

1) WAYFARING STRANGER - PERFORMED BY JACK WHITE (Traditional)
2) LIKE A SONGBIRD THAT HAS FALLEN - PERFORMED BY REELTIME TRAVELERS (Written by Bobby Neuwirth and Henry Burnett), (Reel Time Travelers are: Thomas Sneed, Martha Scanlan, Brandon Story, Heidi Andrade & Roy Andrade)
3) I WISH MY BABY WAS BORN - PERFORMED BY TIM ERIKSEN, RILEY BAUGUS & TIM O'BRIEN (Traditional) Arranged by Anthony Minghella and Henry Burnett. Additional Lyrics by Anthony Minghella.
4) THE SCARLET TIDE - PERFORMED BY ALISON KRAUSS (Written by Elvis Costello and Henry Burnett)
5) THE CUCKOO - PERFORMED BY TIM ERIKSEN & RILEY BAUGUS (Traditional)
6) SITTIN' ON TOP OF THE WORLD - PERFORMED BY JACK WHITE (Written by Walter Jacobs and Lonnie Carter)
7) AM I BORN TO DIE? - PERFORMED BY TIM ERIKSEN (Traditional)
8) YOU WILL BE MY AIN TRUE LOVE - RECORDED BY ALISON KRAUSS (Written and Composed by Sting)
9) I'M GOING HOME - PERFORMED BY SACRED HARP SINGERS AT LIBERTY CHURCH (Writers - Traditional) Arranged by Tim Eriksen
10) NEVER FAR AWAY - PERFORMED BY JACK WHITE (Written by Jack White)
11) CHRISTMAS TIME WILL SOON BE OVER - PERFORMED BY JACK WHITE (Writers - Traditional)
12) RUBY WITH THE EYES THAT SPARKLE - PERFORMED BY STUART DUNCAN AND DIRK POWELL (Traditional) Arranged by Dirk Powell
13) LADY MARGRET - PERFORMED BY CASSIE FRANKLIN (Writers - Traditional) Arranged by Anthony Minghella Henry Burnett and Tim Eriksen
14) GREAT HIGH MOUNTAIN - PERFORMED BY JACK WHITE (Traditional) Arranged by Ralph Stanley
15) ANTHEM - GABRIEL YARED
16) ADA PLAYS - GABRIEL YARED
17) ADA AND INMAN - GABRIEL YARED
18) LOVE THEME - GABRIEL YARED
19) IDUMEA - PERFORMED BY SACRED HARP SINGERS AT LIBERTY CHURCH (Writers - Charles Wesley 1707 Amzi Chapin 1812 Traditional) Arranged by Tim Eriksen