Messianic Jews celebrate all the traditional and Biblical holidays and festivals. So in general terms, we do not celebrate Christmas and Easter. Though of course we acknowledge the birth and resurrection of Messiah, there is no mention in the Scriptures of commanding us to celebrate the dates.
Apparently none of the earliest believers, either Jewish or Gentile celebrated these days either. Also the time of birth of Messiah Yeshua in the scripture the description leads one to believe it was not in what we call December.
We are not against the celebration however! But we do not have Christmas trees or Easter services, although many synagogues have a Resurrection service yearly on the festival of First Fruits, but not on Easter Sunday as that date was actually added to celebration by Roman Emperor Constantine in 325 AD.