Of non-Scriptural Christmas readings, a selection from the Christmas homily of St Leo the Great is most often used. I find myself partial to this excerpt from St Isaac the Syrian:
This Christmas night bestowed peace on the whole world;
So let no one threaten;
This is the night of the Most Gentle One -
Let no one be cruel;
This is the night of the Humble One -
Let no one be proud.
Now is the day of joy -
Let us not revenge;
Now is the day of Good Will -
Let us not be mean.
In this Day of Peace -
Let us not be conquered by anger.
Today the Bountiful impoverished Himself for our sake;
So, rich one, invite the poor to your table.
Today we receive a Gift for which we did not ask;
So let us give alms to those who implore and beg us.
This present Day cast open the heavenly doors to our prayers;
Let us open our door to those who ask our forgiveness.
Today the Divine Being took upon Himself
the seal of our humanity,
In order for humanity to be decorated by the Seal of Divinity.
Blessings on your Christmas Day and Season.