I didn't know this was possible, but I was besieging a German city with some of my cavalry, waiting for my infantry to arrive with siege gear. WEll, the Germans launch an attack on my cavarly. They issue out of the city and I draw them into the nearby plains. I manage to catch and defeat most of the enemy, and before I knew it my cavalry was following his routing units back into the city. I had assumed the gates would shut on me, but they did not. My cavalry poured into the city, charged into his remaining unit by the main city square and took the town. Fantastic! I didn't even have to build siege engines!

Just wanted to let you all know that this is possible.