I always planted them for deer mostly and I never mowed them. It was pretty amazing how much of the plant that the deer ate. The obviously ate the seeds, but they also ate every single leaf, and a good portion of the heads themselves were eaten. I even watched deer picking at fibers on the stocks during the winter.
And on more than one occasion, I watched young bucks rubbing dry, stiff stocks (I've seen them do that with pokeweed, too).
I left my plants standing until late winter when there was nothing left on the plant for deer to utilize. I didn't want to mow the stuff if there was anything that deer would still use. I figured that if I chopped it all up, I would be wasting some tonnage.