Although Christmas did not become an official holiday until five years after the Civil War ended, Wikipedia tells us that Carols, hymns and seasonal songs were sung during the Christmas season, 1861-1865.
If you enjoy Christmas music as much I do, you may be interested in the fact that some of the carols popular during the War are still sung today. Among these are "Deck the Halls", "Oh Come All Ye Faithful", and Mendelssohn's "Hark the Herald Angels sing" (1840),
American musical contributions to the season include "It Came Upon A Midnight Clear" (1850), "Jingle Bells" (1857), "We Three Kings of Orient Are" (1857) and "up on the Housetop" (1860).
Longfellow wrote his pacifist poem, "I Heard The Bells On Christmas Bells" on Christmas Day 1864 after he herd his son had suffered severe wounds during the Mine Run Campaign. The poem was set to music by John Baptiste Calkin after 1872 and is in the established library of Christmas carols. Wikipedia says that Longfellow's carol does not include two stanzas from the original poem that focused on the war.