One of my favorite Christmas hymns from the West is the old Latin hymn Veni, Veni Emmanuel which translates as O Come O Come Emmanuel.......which is often heard by choirs and carolers. It is a beautiful theological hymn reminding us of God's salvation in Christ.
Below are the lyrics for the hymn. The hymn is part of the O Antiphons sung in the Western Church during Vespers. You can learn more about that in the link below. There are a series of hymns beginning with "O" therefore the name "O Antiphons"