Yes! Some of them, at least. The Romans used a somewhat lightly regulated uniform system in the Republic, which would result in some animal pelts being used. It was somewhat barbaric to wear pelts, as the Romans compared fur with living in the countryside. However, there were standardized and more common usage of pelts that I will be getting into primarily.

Firstly, during the Siege of Capua in 212 BC during the second Punic War, a new special unit was introduced:

“out of all the legions were picked young men who by reason of strength and lightness of build were the swiftest. these were furnished with round shields of smaller size than those used by cavalry, and seven javelins apiece four feet long and having iron heads such as are on the spears of the light —armed troops. The horsemen would each of them take one of these men on to their own horses, and they trained them both to ride behind and to leap down nimbly when the signal was given. when thanks to daily practice they seemed to do this with sufficient daring, they advanced into the plain which was situated between the camp and the city wall in the face of the Capuan cavalry in battle —line. and when they had come within range, at a given signal the light —armed leaped to the ground. thereupon an infantry line suddenly dashes out from the cavalry at the enemy's horsemen, and while attacking they hurl one javelin after another.”

You may know these troops as velites! Which would commonly wear almost no armor- besides a helmet. Sometimes, more often than not, they would cover this helmet with a wolf’s pelt to distinguish themselves to officers if they fought ‘pluckily,’ as Polybius puts it. Other times, these lightly armored projectile units would simply just have some form of marking on them to do the same aforementioned thing. Much like the javelins equipped to heavy melee infantry, the javelins that were given to Velites would similarly bend upon impact- becoming useless to throw back.

Another would be the famous Aquilifer, a compound name of aquila, meaning eagle, and fers, meaning to carry. They carried the eagle standard, which was of HUGE importance to the Romans. If that standard was lost, it was seen as a near cataclysmic event. (They only lost 15 of them over the course of their usage.) After all, it was a symbol of the legendary god Jupiter. Much like the velites, (although the velites were retired in the Marian Reforms,) the Aquilifer was given a lion fur pelt to wear. They usually were in charge of the army’s pay. Julius Caesar puts how much influence on the army the aquilifer had when he prepared his landing during the first invasion of Britannia.

”And while our men were hesitating [whether they should advance to the shore], chiefly on account of the depth of the sea, he who carried the eagle of the tenth legion, after supplicating the gods that the matter might turn out favorably to the legion, exclaimed, “Leap, fellow soldiers, unless you wish to betray your eagle to the enemy. I, for my part, will perform my duty to the commonwealth and my general.”

Then, he just… jumped in the drink. It worked, though, as mostly every single soldier that could hear him jumped from the boats to follow the Aquilifer. After the Britons saw this, some had become distressed, and forgot to dismount their horses. Thus, Caesar took the victory with grace.

The next unit that commonly wore animal pelts was the vexillarius; another standard-bearing division. There would typically be more than one vexillarius, one for each cohort (500 men) typically, showing their symbols and cohort names. The first cohort, however, commanded by a Primus Pilus (centurion on steroids essentially!), would typically carry a standard showing the name/symbol of the legion itself, rather than the cohort. The vexillarius would be issued a bear’s pelt to put over their helmet. (they look really cool, here is a reenactor wearing one.)

Sources

Adrian Goldsworthy, The Complete Roman Army

Christopher Matthew, On the Wings of Eagles: The Reforms of Gaius Marius and the Creation of Rome …

Polybius, Histories 6

Plutarch, John Langhorne, William Langhorne, Plutarch’s Lives: Translated from the Original Greek

Julius Caesar, Commentarii De Bello Gallico