It has been pointed out that, if we consider the fact that the Scriptures tell us that the shepherds were “watching their flocks by night” (Luke 2:8), the time Jesus was born could not have been near Christmas when we celebrate his birth, because shepherds don’t have their sheep out in the fields in winter. Nevertheless, it has also been shown that, even today, there are many shepherds in Israel who keep watch over their flocks in the fields at night all year long. What can be said of these things? Is someone lying just to make a point? No, no one is lying, but the point of the phrase is misunderstood.
John the Baptist, who was chosen by God to prepare the way of Jesus, refers to Jesus as the “Lamb of God” (John 1:29, 36). This puts Jesus in the context of a sacrificial lamb, probably the Passover Lamb. Understanding this, it seems logical to believe that the flock of sheep (with the lambs) referred to in Luke 2 also has some symbolism for us in the story of Jesus’ birth, just as other things mentioned refer symbolically to something about Jesus, the Messiah.
Notice what the rabbis have claimed concerning the sheep around Jerusalem during the 1st century AD, before the Temple was destroyed:
If cattle was found in Jerusalem as far as Migdal Eder and within a like distance on any side [of Jerusalem], males [must be considered as being] burnt-offerings, but females [must be considered as] peace-offerings.  R. Judah says: if they were fit for the Passover-offering,  [they must be considered as] Passover-offerings [when found] within thirty days before the Feast [of Passover].  [Babylonian Talmud: Shekalim 7.4]
The sheep in Luke’s narrative are sheep of the Temple, that is, those that are either owned by or would be sold to the priests of the Temple for sacrifices (prefiguring Christ’s sacrifice). Nevertheless, there was certain other criteria that must be met for that to be true. Consider what is written further about what animals were acceptable for sacrificing in the Temple:
“Our Rabbis taught: The following are pasture animals and the following are household animals. Pasture animals are such as are led out about [the time of] Passover and graze in [more distant] meadows, and who are led in at the time of the first rainfall (late October to early November according to our reckoning). The following are household animals: Such as are led out and graze outside the city-border but return and spend the night inside the city-border. Rabbi says: Both of these are household animals; but pasture animals are such as are led out and graze in [more distant] meadows and who do not return to the habitation of men either in summer or in winter.” [Babylonian Talmud: Bietzah 40a – parenthesis and emphasis mine]
Only those animals that were either brought in at night or at the time of the first rainfall were considered fit for the Temple. Therefore, if the sheep (and their lambs) had any significance at all in the birth of Jesus, they would have had to have been those which would have been brought in before the rainfall in the fall. This would show Jesus’ birth couldn’t have been in winter time. Moreover, I have shown elsewhere (see Mary’s Journey to the Hills of Judea) that Mary’s conception could have occurred only in the ninth month of the Jewish calendar (Kislev), and she journeyed to visit Elizabeth during the feast of Hanukkah. This would put the birth of Jesus about the time of the Jewish New Year or on the Feast of Trumpets, which also corresponds to the Scriptures (Revelation 12:1, 5).
 Cf. Genesis 35: 21; Micah 4:8. It is situated south of Jerusalem on the Hebron road
 The finder must offer them as such; cf. supra p. 15, n. 7. Most cattle in Jerusalem and the vicinity were intended for sacrifices
 A male of the sheep or of the goats and one year old; cf. Exodus 12:5
 For during that period such animals were mostly intended for the Passover offering
 Revelation 12:1 describes the sign of Virgo in the heavens. With the moon at the woman’s feet it would be the crescent of the new moon or the first day of the month—i.e. The Feast of Trumpets in the Jewish calendar.