Within our faith there are Traditions with a large T that cannot be changed, like the belief in the immaculate conception, and there are traditions with a little t that are not necessary for the foundation of faith.
Christmas Caroles and many of the nativity scenes that are in circulation are simply traditions with a little t. They do not hinder our faith by causing us to believe differently that the church tells us, but they enrich our celebrations and are thus considered important.
History is very difficult to record. Even today with our mass media we have difficulty finding out exactly what happened and when because each viewer has a different interpretation of the events. I would not be overly concerned with WHEN it happened or if animals were involved, or if singing of the angels occurred. What is important is that Jesus was born, and the lessons and blessings he brought to the world.