Illustrations of Sassanid Persian Clibanarii

[Renatus]

Wouldn't it be more likely that the horses that were collapsing from exhaustion and not the riders?

Both to some extent, according to Zosimus, 1.50.3-4:

'[He] ordered the Roman horse not to engage the fresh Palmyrene cavalry immediately, but to take their charge and pretend to flee until they saw that both their pursuers and their horses were abandoning the chase, exhausted by the heat and the weight of their armour. This is exactly what happened. The emperor’s cavalry obeyed his order, and when they saw the enemy giving up, with the horses wearied and the riders hardly able to move, they checked their horses, wheeled and charged, trampling them as they fell from their mounts.'