Their hats - This word, hat, is found only in this place in the Old Testament. The word סרבל sarbal properly means an outer garment. Herodotus, who lived about one hundred years after Daniel, says, "the dress of the Babylonians consisted of a tunic of linen reaching down to the feet; over this a tunic of woollen; and over all a white short cloak or mantle, χλανιδιον; and on their heads they wore turbans, μιτρησι." Following this, Mr. Parkhurst translates the verse thus: "Then these three men were bound [בסרבליהון besarbaleyhon] in their Cloaks, [פמישיהון patesheyhon] their Turbans, [וכרבלתהון vecharbelathehon] and in their Upper (woollen) Tunics, [ולבושיהון ulebushehon] and their Under (linen) Tunics." And as, according to this interpretation, their סרבלי sarbaley were their outermost garments, we see the propriety with which it is observed at Daniel 3:27 that these were not changed by the fire.

in their. Herodotus says the Babylonish dress was a linen tunic, another of woollen, a white short cloak, and a turban.

coats. or, mantles. hats. or, turbans.

The Song of the Three Children
DANIEL iii. 16, 17, 18. O Nebuchadnezzar, we are not careful to answer thee in this matter. If it be so, our God whom we serve is able to deliver us from the burning fiery furnace; and He will deliver us out of thine hand, O king. But if not, be it known unto thee, O king, that we will not serve thy gods, nor worship the golden image which thou hast set up. We read this morning, instead of the Te Deum, the Song of the Three Children, beginning, 'Oh all ye works of the Lord, bless ye the Lord: praise …
Charles Kingsley—The Good News of God

Daniel
Daniel is called a prophet in the New Testament (Matt. xxiv. 15). In the Hebrew Bible, however, the book called by his name appears not among the prophets, but among "the writings," between Esther and Ezra. The Greek version placed it between the major and the minor prophets, and this has determined its position in modern versions. The book is both like and unlike the prophetic books. It is like them in its passionate belief in the overruling Providence of God and in the sure consummation of His …
John Edgar McFadyen—Introduction to the Old Testament