There is an incident from the Roman siege of Capua in 211 BC during the 2nd Punic War
which mentions skirmishers mounted in tandem with cavalrymen. In fighting around the
besieged city, the Romans infantry are usually successful against the Campanian foot,
but their cavalry are unable to beat the Campanian horse.

Livy 26.4:
A plan was at length adopted, by which their deficiency in strength might be
compensated by stratagem. Young men were selected from all the legions,
who, from the vigour and activity of their bodies, excelled in swiftness; these
were supplied with bucklers shorter than those worn by horsemen, and seven
javelins each, four feet in length, and pointed with steel in the same manner
as the spears used by light-armed troops. The cavalry taking one of these each
upon their horses, accustomed them to ride behind them, and to leap down nimbly
when the signal was given. When, by daily practice, they appeared to be able to
do this in an orderly manner, they advanced into the plain between the camp and
the walls, against the cavalry of the Campanians, who stood there prepared for
action. As soon as they came within a dart's cast, on a signal given, the light troops
leaped down, when a line of infantry formed out of the body of horse suddenly
rushed upon the cavalry of the enemy, and discharged their javelins one after
another with great rapidity; which being thrown in great numbers upon men and
horses indiscriminately, wounded a great many. The sudden and unsuspected
nature of the attack, however, occasioned still greater terror; and the cavalry
charging them, thus panic-struck, chased them with great slaughter as far as
their gates.
However, there is no indication in the sources that this experiment was repeated.