The dating of Christmas is not pagan or arbitrary. The early church father St Ephraim the Syrian, writing in the mid 4th century, states in his Rythm the 4th concerning Christ's conception:
"Moses shut up a lamb in the month Nisan on the tenth day; a type this of the Son that came into the womb and shut Himself"--St Ephraim the Syrian, Rhythm the fourth (p.27)
The significance of this is that the 10th of Nisan can fall in either early April or late March. The 10th according to the torah in Exodus 12 was the day the passover lamb was to be selected.
"This month shall be to you the beginning of months: it shall be the first in the months of the year. Speak ye to the whole assembly of the children of Israel, and say to them: On the tenth day of this month let every man take a lamb by their families and houses."
Now this year, 2010, the 10th of Nisan fell on the 25th of March, (Here is a link to the Hebrew-Gregorian Calendar converter, a Jewish website.) this is the feast of the Annunciation on the Church Calendar. The Feast of the Annunciation is the celebration of the Incarnation, when Christ was conceived in the womb of the Blessed Virgin Mary.
Now assuming Christ went thru the standard gestation period of almost nine months, as most humans do, then he would have been born on or around December 25, if we are to use our modern calendar his gestation would be about 275 days, which is only 9 days longer than average, but still within a reasonable time frame for birth.
Now some believe that since there were shepherds in the fields when Christ was born that therefore He was not born in December, reasoning it would be foolish to keep a flock out in the winter. However, according to the 19th century convert from Judaism, Alfred Edersheim in his book "The life and times of Jesus the Messiah, Volume 1" pages 186-7 he states:
the Messiah was to be born in Bethlehem, was a settled conviction. Equally so was the belief, that He was to be revealed from Migdal Eder, ' the tower of the flock.'a This Migdal Eder was not the watch-tower for the ordinary flocks which pastured on the barren sheep-ground beyond Bethlehem, but lay close to the town, on the road to Jerusalem.A passage in the Mishnah leads to the conclusion, that the flocks, which pastured there, were destined for Templesacrifices, and, accordingly, that the shepherds, who watched over them, were not ordinary shepherds. The latter were under the ban of Rabbinism,' on account of their necessary isolation from religious ordinances, and their manner of life, which rendered strict legal observance unlikely, if not absolutely impossible. The same Mishnic passage also leads us to infer, that these flocks lay out all the year round, since they are spoken of as in the fields thirty days before the Passover—that is, in the month of February, when in Palestine the average rainfall is nearly greatest. Thus, Jewish tradition in some dim manner apprehended the first revelation of the Messiah from that Migdal Eder, where shepherds watched the Temple-flocks all the year round. Of the deep symbolic significance of such a coincidence, it is needless to speak. It was, then, on that 'wintry night' of the 25th of December, that shepherds watched the flocks destined for sacrificial services, in the very place consecrated by tradition as that where the Messiah was to be first revealed."
He further notes that:
"There is no adequate reason for questioning the historical accuracy of this date. The objections generally made rest on grounds, which seem to me historically untenable. The subject has been fully discussed in an article by Cassel in Herzog's Real. Ency. xvii. pp. 588-594. But a curious piece of evidence comes to us from a Jewish source. In the addition to the Megillath Taanith (ed. Warsh. p. 20 a), the 9th Tebet is marked as a fast day, and it is added, that the reason for this is not stated. Now, Jewish chronologists have fixed on that day as that of Christ's birth, and it is remarkable that, between the years 500 and 816 A.d. the 25th of December fell no less than twelve times on the 9th Tebet. If the 9th Tebet, or 25th December, was regarded as the birthday of Christ, we can understand the concealment about it. Comp. Zunz, Ritus d. Synag. Gottesd. p. 126."