As many people would have traveled to Bethlehem for the census, all the houses or certainly upper levels were full. Many people think that Jesus was probably born in September or October during Sukkot, the Jewish Feast of Tabernacles, rather than during December. During the festival, Jews live outside in temporary shelters (the word 'tabernacle' come from a latin word meaning 'booth' or 'hut').
So Joseph and Mary probably had to sleep with the animals on the low level (where it’s common to have a manger cut into a wall where you put the animal food) or possibly (but unlikely) out in a stable, cave or even a covered market stall that sold animals (these stalls could be rented during tabernacles).
It was the custom in those times to wrap a newborn baby very tightly in long bandages called swaddling clothes. The arms and legs of the baby were also wrapped, so they couldn't move. This was done because they thought it helped the baby to grow strong, straight limbs! And as no proper crib was available, the new baby boy was placed in a manger, or feeding trough.
There's a theory that Jesus might have been born a couple of miles outside of Bethlehem where there was a special shepherds' watch tower called the Migdal Eder. So Jesus might have been born out with the shepherds.
It's also quite likely that Jesus was actually born in the autumn (during Tabernacles), not in the winter! It can get very cold in the winter in Israel and it is thought that the census would have most likely taken place during the spring or autumn, at a when many pilgrims, from all over the country, came to visit Jerusalem (which is about six miles from Bethlehem).
Some more facts and details to look at and ponder over the birth of our Savior.
Hugs prayers and God Bless
Izzy
izzy