By definition this question would be best asked on Christianity.SE and it has. What is clear is that he was probably born in the spring or summer as that is when shepherds watch over their flocks (Luke 2:8). March 28 is far more plausible than December 25.
They watched over their flocks in the field in the spring because that is when there was food. Other times, the sheep were brought food - especially in the winter:
One of the principal
duties at all seasons of the year is for the shepherd to plan food for
his flock. In the springtime there is an abundance of green pasture,
and usually the sheep are allowed to graze near to the village where
the shepherd's home is located. After the grain is reaped, and the
poor have had an opportunity to glean what is left for them, then the
shepherd brings in his flock, and the sheep feed on certain fresh
growths, or dried blades, or an occasional ear of grain that the
reapers may have left, or was overlooked by the gleaners. When this
source of food is exhausted then the pasture is sought in other
places. The wilderness of Judea which is located along the western
side of the Jordan Valley is carpeted in the spring with a certain
amount of grass and this turns into standing hay as the hot weather
comes, and this becomes food for the sheep during part of the
summer.12 Scripture often refers to shepherds looking for pasture for
their flocks. "And they went to the entrance of Gedor, even unto the
east side of the valley, to seek pasture for their flocks" (I
Chronicles 4:39). The Psalmist thanks GOD for the pasturage which the
LORD as Shepherd provides for His people: "So we thy people and sheep
of thy pasture will give thee thanks for ever" (Psalm 79:13). In the
late autumn or winter months, there are times when the shepherd can
find no pasturage that is available for his flock, and then he must
become responsible for feeding the animals himself. If the flock is
small there may be times when it is stabled within the peasant house,
and the family lives on a sort of mezzanine floor above it. At such
seasons of the year the shepherd must provide the food. This is what
Isaiah meant when he said: "He shall feed his flock like a shepherd"
(Isaiah 40:11). In some sections of Syria, flocks are taken at this
season to places in the mountain country, where the shepherd busies
himself with the bushy trees, cutting down branches that have green
leaves or tender twigs, that the sheep and goats can eat. Micah was
probably speaking of this custom of providing food for the sheep, when
he said: "Feed thy people with thy rod, the flock of thine heritage"
(Micah 7:14). [Manners And Customs of Bible Lands]
Secondly December 25th is not a birthday party. It's a feast day to celebrate the incarnation of the logos. I'm not sure that any denomination says that his birthday was in December. I'm very confident that the bible does not claim that this was his birthday. Please, do not bring your noise makers and cone hats, it's not a birthday party.
Father Edward McNamara, professor of liturgy at the Regina Apostolorum Pontifical University has a nice question and answer here. It may even suggest a possible relationship to March 28th:
In fact, both Christmas and the Annunciation celebrate different
aspects of the mystery of the Incarnation and do so with relatively
little attention to biological or chronological precision.
The feast of Christmas originated in the city of Rome and was first
celebrated about the year 330, some 15 years after the end of the
persecutions, and, perhaps, in the recently completed basilica of St.
Peter's.
The earliest traces of a feast of the Annunciation are found in Egypt
in 624. The testimonies increase after that date in various areas of
Christendom. From the beginning it was celebrated on March 25 due to
the belief that the spring equinox was both the day of the creation
and of the start of the new creation in Christ.
This date caused a difficulty for some Churches, such as the Spanish
Mozarabic rite and the Ambrosian rite of Milan, due to their strict
prohibition of all festivities during Lent. They thus opted for
celebrating the Annunciation on Dec. 18, a practice that continues to
this day.