Always appreciate my Orthodox brothers' perspective on things. Even though I am not Orthodox, your understanding of this coincides with mine. Regrettably, there are many Christians on FR who appear to insist that sort of thing must be observed alongside of the Incarnation...
The icon always has an ox and an ass, as Kolo mentions. These are not randomly chosen animals, but rather represent a direct reference to the words of Isaiah 1:3, where the Prophet writes -- "The ox knoweth his owner, and the ass his master's crib..."
Unlike Western artistic portrayals of the Nativity, traditional Orthodox iconography has the Virgin and Christ at the very center of the icon, whereas St. Joseph the Betrothed is off in the lower left hand corner of the icon. It is thereby made clear that he is not the father of the child. In addition, he looks troubled, and there is the figure of an old man standing in front of him, representing Satan, who tempted Joseph to doubt the words of the angel that had told him that the child was of God.
The characters at the lower right of the icon are usually of women midwives, who are washing Jesus, adding yet another layer of emphasis to the reality that Jesus was born physically -- and that his arrival on earth wasn't something merely mystical and symbolic.
There is usually a tree beneath Christ, which both signifies that He is the one prophesied to arise from the root of Jesse, and also is a prefiguring of the Cross.
The wise men, who arrived later, are off in the distance, while the simple shepherds, to whom the birth was first announced, are closer -- as well as being a reflection of the Gospel account, it also shows that the "common and simple folk" often have an easier and more direct route to being close to God than do the "wealthy and wise."
This is truly one of the richest icons in all of Orthodox iconography. And there is truly nothing sentimental about it...
The cosmic implications of the Nativity are also reflected in the hymnology of the Feast. The Troparion/Apolytikion of the Feast goes:
Thy Nativity, O Christ our God, hath shown to the world the light of wisdom. For by it, those who worshipped the stars were taught by a star to adore Thee, the Son of Righteousness, and to know Thee, the Orient from on high. O Lord, glory be to Thee."
The Kontakion of the Feast:
Today the Virgin gives birth to the Transcendent One, and the earth offers a cave to the Unapproachable One. Angels and shepherds glorify Him, and the magi journey with the star. For our sake, the pre-eternal God is born as a little Child."
The Exapostilarion sung at the Vigil:
From on high our Savior, the Dayspring of the East, hath visited us, and we who are in darkness and shadow have truly found Him: for the Lord hath been born of the Virgin."
And finally, a beautiful sticheron from the Praises of the Vigil:
Today Christ is born of the Virgin in Bethlehem. Today He who knows no beginning now begins to be, and the Word is made flesh. The powers of heaven greatly rejoice, and the earth with mankind makes glad. The Magi offer gifts, the shepherds proclaim the marvel, and we cry aloud without ceasing: Glory to God in the highest, and on earth peace, good will among men.
Of course, all of it is even more beautiful when sung.
Wishing all a blessed preparation for the Nativity...
About the continuity of the Old and the New Testaments
By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and aging will soon disappear. (Heb 7,13)
Here Jesus directly invalidates the OT verses Exodus 21:24; Lev. 24:20; Deut. 19:21 and reinterprets them as something we should not follow:
Kolokotronis is absolutely on the mark when he says that Orthodox Christmas is not commercialized, always staying focused on Christ.
Thus, rather than wishing someone "Merry Christmas" we greet each other with "Christ is born!" and instead of "Marry Christmas to you too" we respond "Indeed, He is born!" This is not our personal holiday of merrymaking, but a celebration of the birth of our Saviour. It's not about us, Santa or sales.
Thus Christmas to the Orthodox has a different name and a different meaning: it is simply and always "The Birth of Christ."
Likewise, Orthodox Easter is not even called that, but "Resurrection." It is the central feast of the Church, eclipsing even His Birth. And, consistent with the focus on our Saviour, we do not wish each other "Happy Easter" (the word Easter is pagan), but rather exclaim "Christ is risen!" to which we reply "Indeed, He is risen!"
And God in His wisdom has assisted in the preservation of that by keeping the calendars separate
Many blessings