What did the Romans build for there army soilders to ride in?

Answer 1

Nothing. The Roman army did not ride, they walked or marched. They had carts and wagons, but those were for the wounded or the very ill. An officer of a high rank on occasion could ride in a small carriage.

Answer 2

The Romans built chariots and later on, they developed and used various types of cavalry units, including horse-mounted soldiers called equites. They also built siege engines, such as catapults and ballistae, to assist their armies in attacking fortified positions. Additionally, the Romans used ships and boats for naval warfare, including galleys and triremes.