A few bits. Firstly there was no census at the time of the birth of Jesus. Historically the nearest census was about ten years adrift of the alleged date of the birth, long after the wicked King Herod had died - and that didn’t require everyone to return to the place of their birth to register. There’s no record of Herod’s slaughter of the innocents either.
Secondly, there was no stable. The wise men visited the baby at a house. The manger was possibly handy because it wasn’t unknown for people in that area of the world to share their homes/caves with their animals. Some still do. Thirdly, low winter (and night) temperatures in Israel are not unusual. Snow is not unknown.
All of that said, whilst I’m pretty much convinced that Jesus existed, the legend surrounding him has been shamelessly fabricated, much of it designed to tug at the heartstrings, as the story of Christmas (and that of the crucifixion) does – and it works. Personally I have a sneaking suspicion that Jesus was a man who would have been deemed pretty special – the rightful king of the Jews - hence Herod's pursuit of him. There was a fellow who wanted to hang on to his throne.
As fascinating as it is (to me at least) to try to make some sense of it all, the story, written long after the event, renders it one giant, complex, jigsaw puzzle - probably impossible to ever solve completely.