The Bible itself proves in Song of Solomon 2:11, and Ezra 10:9,
and 13, that winter was a rainy season not permitting shepherds
to abide in open fields at night.
That doesn’t really prove anything. The job of a shepherd continues regardless of rain, sleet or snow. In London, there is an Underground station known as Shepherd’s Bush. It takes its name from bushes, and later hedges, that were trimmed so as to feature a cut-out providing shepherds with a rudimentary shelter from the elements.
Also, furthermore, just because it is a rainy season does not mean it was raining that particular night.
Finally, it really doesn’t matter; Christmas is a liturgical celebration of the Nativity, and originally all the churches adhered to the practice, surviving only in the Armenian Church, of celebrating the Nativity together with the Baptism of Christ on the Feast of the Theophany on January 6th (which in the Western Church was later redefined to be about the Three Wise Men, and became known as Epiphany).
The date of December 25th for the birthday of our Lord was derived from an ancient pan-Mediterranean belief that important people were conceived on the same date that they died, thus, since our Lord was crucified on the 14th of Nissan, which is approximately March 25th, this provided the date for the Feast of the Annunciation, which also predates the Feast of the Nativity, but when most of the churches, except for Armenia, decided to separate the Nativity and Theophany (Baptism of Christ) into two different feasts, they simply added nine months to March 25th.
In Orthodox Churches which still use the Julian Calendar for everything, it is possible for the Annunciation and Pascha (Easter) to occur on the same day, which happens about every 49 years and is known as a Kyriopascha. The last one occurred in 1990 or 91, before the collapse of the Sovietsky Soyuza (because of the economic malaise which followed, and also coincidental unpleasantness following previous Kyriopaschae, some people of the former USSR and surrounding lands now superstitiously regard a Kyriopascha as bad luck, but this is of course not the case).
I was very disappointed in 2016 when those Eastern Orthodox Churches, in Finland and Estonia, that use the Gregorian Calendar exclusively, including for the calculation of Pascha, as well as the majority of the Byzantine Rite Catholic Churches, which are also on the Gregorian Calendar* did not celebrate the Kyriopascha that occurred that year according to that calendar (as far as I am aware).
A Kyriopascha is of course impossible in those Orthodox Churches such as the Antiochian, Romanian, Bulgarian, and the Greek Orthodox Archdiocese of North America, which use the Gregorian calendar as the basis for determining fixed holy days defined whose services are contained in the hymnal known as the Menaion like Michaelmas, Christmas, Theophany, Candlemas, the Annunciation, the Holy Apostles, the Transfiguration and the Dormition, but use the Julian calendar for determining the date of Pascha (and thus the use of the Triodion hymnal, containing the hymns for pre-Lenten period, the Great Lent and Holy Week, and the Pentecostarion hymnal, also known as the Flowery Triodion, which contains the hymns from Pascha Sunday through the Pentecost, ending on the Sunday after the Feast of All Saints, which is the first Sunday after Pentecost, corresponding to Trinity Sunday in the West). This system of using the Julian Calendar for the movable feasts and the Gregorian for tne fixed feasts is also employed by the Syriac Orthodox Patriarchate of Antioch, except in Jerusalem, where all churches except the Roman Catholic Church and the Protestants use the Julian calendar exclusively, and I think in India, where if memory serves all of the St. Thomas Christians use the Gregorian calendar, as far as I am aware (
@coorilose can confirm this).
In general, I think it works better when churches use either the Julian Calendar exclusively, as is done in Jerusalem, and by the Copts** (Egyptian Christians), Ethiopians, Eritreans, Serbians, Russians, Ukrainians, and Athonite Monks, or the Gregorian calendar exclusively, which is the practice of the Armenians outside of Armenia, the Finns, Estonians, Maronites (Lebanese Catholics distantly related to the Syriac Orthodox), and nearly all Western Christians***, as well as the Assyrian Church of the East, which switched to the Gregorian Calendar in the 1960s (for a time, the offshoot Ancient Church of the East continued using the Julian Calendar, but I am not sure if that is still the case, as I heard they had discontinued using it in preparation for reunification of the two Assyrian churches).
* the most notable exception to this being the massive Ukrainian Greek Catholic Church, which uses only the Julian Calendar, just like the Russian Orthodox Church and the canonical Ukrainian Orthodox Church
** Technically the Copts use the Coptic Calendar, which is the same length as the Julian Calendar and is fully in alignment with it, but has different names for the months and a different epoch, the Year of Martyrs, dated from the start of the Diocletian Persecution. The last feature I rather like, and wish other churches would adopt, seeing that we have established throughly that our Lord could not have been born in 1 AD, as by that time Augustus was dead, and based on information in the Gospels of Luke and Matthew His birth is usually estimated as being between 6 BC and 4 BC.
*** The sole remaining exception I am aware of to Gregorian Calendar use among Western Christians is in the Western Rite of the Russian Orthodox Church Abroad. However, it is worth noting that when the Gregorian Calendar first appeared, there was a widespread reluctance and refusal among the early Protestants to adopt it, but this opposition softened in time for various sociopolitical reasons. That said if there exists somewhere a small church of hardcore Old Calendarist Presbyterians or Baptists using the Julian Calendar, that would be thrilling,
