The Centurion and his horse questions.

[jvrjenivs]

These are all interesting citations John, but actually only tells us that there were experienced centurios who know to ride. When on march, someone has to go ahead and check for a good site for the next camp or to get intelligence. These scouts therefore must be highly moveable, so were mounted (at least knew to ride and probably all had a horse). Those experienced officers (including centurios as in your citation) who were going to look in advance of the column had to be mounted. This doesn't tell you anything about the lower centurio, which not leaves the column.

Here a stele of a exploratores who was mounted.

(unfortunatelly I don't have a source of that stele) but probably it is in the database on the mainsite.)