Alfred Edersheim accepts the traditional date based on the following historical evidence:
At the outset it must be admitted, that absolute certainty is impossible as to the exact date of Christ’s Nativity - the precise year even, and still more the month and the day. But in regard to the year, we possess such data as to invest it with such probability, as almost to amount to certainty. ...6. Lastly, we reach the same goal if we follow the historically somewhat uncertain guidance of the date of the Birth of the Baptist, as furnished in this notice (St. Luke i. 5) of his annunication to his father, that Zacharias officiated in the Temple as on of ‘the course of Abia’ (see here vol. i. p. 135). In Taan. 29 a we have the notice, with which that of Josephus agrees (War vi. 4. 1. 5), that at the time of the destruction of the Temple ‘the course of Jehoiarib,’ which was the first of the priestly courses, was on duty. That was on the 9-10 Ab of the year 823 A.U.C., or the 5th August of the year 70 of our era. If this calculation be correct (of which, however, we cannot feel quite sure), then counting ‘the courses’ of priests backwards, the course of Abia would, in the year 748 A.U.C. (the year before the birth of Christ) have been on duty from the 2nd to the 9th of October. This also would place the birth of Christ in the end of December of the following year (749), taking the expression ‘sixth month’ in St. Luke i. 26, 36, in the sense of the running month (from the 5th to the 6th month, comp. St. Luke i. 24). But we repeat that absolute reliance cannot be placed on such calculations, at least so far as regards month and day. (Comp. here generally Wieseler, Synopse, and his Beiträge.) (Life and Times of Jesus the Messiah, Appendix VII.)
It also doesn't get around the issue of the fact that the sheep and their shepherds weren't still out in the field come December due to it being Israel's rainy season, and being pretty darn cold up in the mountains. To quote Adam Clark:
It was a custom among the Jews to send out their sheep to the deserts [wilderness], about the passover [sic], and bring them home at the commencement of the first rain: during the time they were out, the shepherds watched them night and day. As the passover [sic] occurred in the spring, and the first rain began early in the month of Marchesvan, which answers to part of our October and November, we find that the sheep were kept out in the open country during the whole of the summer. And as these shepherds had not yet brought home their flocks, it is a presumptive argument that October had not yet commenced, and that, consequently, our Lord was not born on the 25th of December, when no flocks were out in the fields; nor could He have been born later than September, as the flocks were still in the fields by night. On this very ground the nativity in December should be given up. The feeding of the flocks by night in the fields is a chronological fact, which casts considerable light on this disputed point. (Clarke's Commentary, vol. V, p. 370)Shalom.