Plato recommends it for health, as also Pliny says it is good for the stomach and the joints.

Let us go further into this matter since here we are.
We read in Xenophon a law forbidding any one who was master of a horse to travel on foot.

Trogus Pompeius and Justin say that the Parthians were wont to perform all offices and ceremonies, not only in war but also all affairs whether public or private, make bargains, confer, entertain, take the air, and all on horseback; and that the greatest distinction betwixt freemen and slaves amongst them was that the one rode on horseback and the other went on foot, an institution of which King Cyrus was the founder.
There are several examples in the Roman history (and Suetonius more particularly observes it of Caesar) of captains who, on pressing occasions, commanded their cavalry to alight, both by that means to take from them all hopes of flight, as also for the advantage they hoped in this sort of fight.
"Quo baud dubie superat Romanus," ["Wherein the Roman does questionless excel."-- Livy, ix.

22.] says Livy.

And so the first thing they did to prevent the mutinies and insurrections of nations of late conquest was to take from them their arms and horses, and therefore it is that we so often meet in Caesar: "Arma proferri, jumenta produci, obsides dari jubet." ["He commanded the arms to be produced, the horses brought out, hostages to be given."-- De Bello Gall., vii.