He was born in the early summer of 4 BCE. It was during the reign of Herod, and during the Roman census. Also- the book of Luke says he was born "as shepherds watched over their flocks by night." In a warm area like Judea, the summer sun is too hot for wool-covered sheep, so they stay in the barns during the day and graze at night when it's cool. So if the shepherds were out watching over the flock at night, it had to have been during the summer.