The Centurion and his horse questions.

[jkaler48]

Here is another example of a Centurion who is mounted for a special detail:
Flavius Arrianus Acies contra Alanos
"Behind them the German cavalrymen, these too in two divisions, and a centurion should command them, the one in charge of the camp."
Since he is probably the Camp Perfect he may have been chosen for this duty in part because he was already mounted by reason of his senior position.

And these Centurions were probably also mounted:
"The picked cavalrymen should be with Xenophoon himself, and two hundred infantrymen from the legion, the bodyguards, and the centurions attached to the picked cavalrymen and the commanders of the bodyguards and the decurions of the elite soldiers."