How well do horses fare against tanks - anyone know? Tanks are really big and bulky and I'm sure (well-trained) horses could literally run circles around them, which wouldn't do any good because how would you get through the armor.

A cavalry charge was tried once in the opening days of WW1. A machine gun took care of it. Tanks have machine guns.

P.S. Horses where then relegated to hauling equipment around, not combat. This persisted even into WW2. The Germans used horses extensively for transport. You don't see it much in the documentary films, as the cameramen were instructed to not show the horse drawn stuff. They wanted to present the image that the Wehrmacht was mechanized.