The Centurion and his horse questions.

[D B Campbell]

Of course while it may have been more difficult to do so if they were on foot rather than mounted it still doesn't amount to proof about the base question about Centurion's having been mounted on the march.

How difficult would it be to advance with the scouts to select a site for the camp? (Caesar, Gallic War 2.17: "[Caesar] sent forward scouts and centurions, who were to select a suitable site for the camp".) Maybe they just hitched a ride?