Another reason why they needed to be light is that the harness was not invented until around 500 AD. Therefore those horses were pushing on a bar which was lit

Another reason why they needed to be light is that the harness was not invented until around 500 AD. Therefore those horses were pushing on a bar which was literally cutting their windpipes off. This severely limited the poor beast's strength. We can tell when the harness was invented because horse drawn carts suddenly double in size. It's amazing how much more work a horse can do when it can breathe!