Scripture says the shepherds were in the fields outside Bethlehem. That means it was after the rains started and the grass was growing. The rainey season starts in November and the pastures are ready for grazing starting in December. Turns out December 25 could be correct.
I thought they normally collected their taxes/census in summer
One of my instructors at the seminary stated that it is even possible/ likely that there were shepherds that maintained the temple flock which was used for the regular sacrifice.
Luk 2:22 And when the time came for their purification according to the Law of Moses, they brought him up to Jerusalem to present him to the Lord Luk 2:23 (as it is written in the Law of the Lord, "Every male who first opens the womb shall be called holy to the Lord") Luk 2:24 and to offer a sacrifice according to what is said in the Law of the Lord, "a pair of turtledoves, or two young pigeons."
Due to his station in life Joseph would have had to offer a smaller sacrifice as outlined in the OT. Wealthier people would have had to offer more or they could have been for the priestly sacrifices as well.