Can I simply run a mower over my peonies in late fall, I know I can, but will it do any damage. They are small plants that produce two or three flowers each.
As long as you don't mow too close to the ground and don't damage the rootball and the new eyes for next spring mowing over them is fine. You'll probably want to remove all of the dead stalks afterward, though, unless you're using a bagging mower which does it for you! I haven't done it before but have seen posts where some people mow them down every year with no negative impact at all. I assume they're all herbaceous? You wouldn't want to mow over a small tree peony.