Based on this link Australian forces did not use horse-equiped forces in large numbers in WWII. All CAV units were trained as motorized/armored troops from the outset, it seems. For instance the 6th Division Cav Regiment was formed in 1939, and trained on machine-gun carriers and, from October, six old Vickers light tanks. I'm sure Epa's sources are better than mine, given the fact that we're talking ANZAC here, so I assume horse-equipped forces did see some action. But according to this source fully horse-equiped forces were no longer an option for the Australian army, as the number of horses that were available for military use had seriously declined between the wars.