As long time readers of "Ex Corde Ecclesiae" know, I have never forgiven the Council of Trent for eliminating all but a handful of sequences. Christmas is a glaring hole in the liturgical calender. Although it is a big feast for ordinary folk in the pews, it does not merit a sequence in wither the Missal of John XXIII or Paul VI.
Sequences are lengthy chants that should follow the Gospel Alleluia, hence the name "sequence." (The General Instruction seems to require that order be reversed in the Ordinary Form of the Roman Rite which makes no sense liturgically, musically, or historically.) As I see it, the sequences' main function is to give musical coverage for a more elaborate gospel procession on special feasts or in big Cathedrals. Sequences are a "drawing out' of the Alleluia verse while the procession processes. Their cadence suits a procession.
It turns out there is a Christmas sequence and it is not a liturgical fossil. It is the Eleventh Century chant, "Laurabundus." It is still in the Dominican Missal, which is one of the uses of the Roman Rite
Jeffrey Tucker alerts us to its existence and has posted a video of its being sung. Read "Sweeten Your Christmas Song: Laetabundus."