Theophylact of Ohrid

These shepherds are a type of the spiritual shepherds — the bishops. Thus, bishops must guard their flock and play, that is, sing something spiritual and teach the people, and then they will be deemed worthy of divine visions and hearings.

Commentary on Luke ↗

Ancient Greek Expositor

The shepherds were filled with astonishment at the things that they saw and heard, and so they left their sheep-folds, and set out by night to Bethlehem, seeking for the light of the Saviour; and therefore it is said, They spoke one to another, &c.

Catena Aurea by Aquinas ↗

Bede

And it happened that as the angels went away from them into heaven, the shepherds spoke to one another. Let us go over to Bethlehem and see this word that has happened, which the Lord has made and shown to us. Consider carefully how reasonable are the words of the shepherds, and worthy of the pastors of the Church. For indeed, as if keeping watch, they did not say: Let us see the child, let us see what is said, but: Let us see the word that has happened: In the beginning was the Word, and the Word became flesh (John 1). …

On the Gospel of Luke ↗

Bonaventure

As for the mutual exchange of exhortation, it is said: And it came to pass, when the Angels had departed from them into heaven, the shepherds spoke to one another, namely exhorting one another, according to Hebrews 3: "See to it, brothers, that there not be in any of you an evil heart of unbelief, but exhort one another every day." And rightly so, because "iron is sharpened by iron, and a man sharpens the face of his friend." As for the rectitude of intention, it is added secondly: Let us go over to Bethlehem and see this word that …

Commentary on Luke, Chapter 2 ↗