I think the Armenians may be the only ones who do it. Here's a small article about it which I received in my email a few weeks ago. I know the person who sent it, but not the source of the original piece.
You recently commented on the Eastern Churches' dating of the Feast of
the Nativity of our Lord (or Christmas). I'm not sure if you are aware
of the Armenian Church's traditional practice regarding this Feast.
Please allow me to elaborate.
Leaving the issue of "calendars" aside (which is not standarized
throughout the Armenian Church), the Armenian Church (to the best of my
knowledge) is the only ancient Church which maintains the ancient dating
of the Nativity on January 6th. Allow me to quote an Armenian text,
"Saints and Sacraments of the Armenian Church," in which the author,
Bishop Kaloustian writes,
"The reason for changing [the Nativity from January 6th to December 25th]
is given [by a Roman Catholic] author:
'The Lord was born in the month of January on the same day on which we
celebrate the Epiphany, for, of old, the feast of the Nativity and
Epiphany were kept on one and the same day. The reason why our Fathers
changed the solemnity celebrated on the sixth of January, and transfered
it to the 25th of December is as follows: It was the custom of pagans to
celebrate the birthday of the Sun on this very day, December 25th. In
these solemnities and festival the Christians too were tempted to
participate. The leaders of the Church, therefore, decided that the
Birth of Christ, be kept on this date (i.e. 25th of December) to
overshadow the pagan festival and on Januarty sixth, the feast of
Epiphanies. (Catholic Encyclopedia: Articles, "Christmas" and
Bishop Kaluostian continues:
"This change, having begun in Rome, spread very quickly to the East and
all over the Roman Empire. The change did not penetrate into Armenia,
because the Armenians, having no such pagan festival on December 25th to
suppress, did not see any reason for following the new practice... the
Armenians wanted to remain faithful to the ancient custom; so they have
kept the old date throught the centuris to the present day." (pgs.62-63).
Thus on the 6th of January (whichever calendar they are using) Armenians
celebrate the Nativity (Birth) and Theophany (Baptism) of Christ in one
solemn Divne Liturgy as is the anceint tradition. Besides the conjecture
of whether this was actually "the day" of Christ's Birth, I hope this
helps to round out your information on the Eastern Churches dating and
celebration of the Nativity of our Lord.