Exactly - a shadow picture, just as was Passover for the sacrifice. It's why the Almighty instructed us to always observe these dates!
They are also shadows of events to yet to come.
Christ fulfilled all “the shadows” of things to come. I don’t think he at all minds when we celebrate His birth, rather that we understand why HE came and His purposes.
Rather like people attempting to put a date on His second coming....we see the signs...which as at his birth were significant and with much meaning....but HE’s chosen not to tell us exactly when.
So too His birth...we can get a general idea but to get caught up in when exactly He was born is to miss the message of the “Good News”....and it is that Good news we celebrate...”A Savior is Born”....and generally when Christians do celebrate the Savior’s arrival.
I personally believe The Messiah was born in the 1st day of God’s calendar 6th month. Exactly 40 days before the Day of Atonement - where on the day of Atonement He was dedicated At the temple after the circumcision and the day purification of Miriam. They would still be in the area or Tabernacles for him to dwell as John put it...
ALL of the Jewish feasts mandated in the bible are either prophetic telling what will someday happen or in remembrance of events concerning Christ which have already happened. They are part of Gods regularly scheduled events to keep us fully aware of Christ and major events concerning Him.
It is extremely unfortunate that the Romans wanted to replace all of Gods mandated feasts with ‘holy’ days of their own creation thereby impacting us on exactly what He wants us to remember.