Hi Susie, welcome to the peony forum! It is a good idea to cut back the dead/dying foliage on peonies in the fall. If the leaves are browning or the shrub looks like it's dying it's the perfect time. You can cut them back to an inch or 2 above the ground for herbaceous peonies; those stems are done and you'll get all new growth from the roots next spring. If you're in a damp climate cutting them back severely in the fall will probably get rid of any potential mildew problems. Plus they just don't look very good once they start dying back!
If you're in a dry climate it doesn't hurt to leave them to the spring and cut them back when you start seeing new growth. Here in Denver we don't have many problems associated with moisture so I normally wait until spring. That's mainly because I'm a lazy fall gardener and enthusiastic spring gardener; especially after all of the fall planting I don't want to do anything else!
I assume your peonies are herbaceous, that's the most common type. If your peonies have a woody stem like a tree branch it's a tree peony and those don't require any pruning although you can a bit to shape it if you want. The stems on herbaceous are normally green or reddish, tree peonies will have a main stem that is brown and barky, only new growth is green.
Kousa uses an organic bulb fertilizer with great results on her peonies, I haven't ever yet but plan to next spring. Have the name she uses written down but no where near me now! Hopefully she'll respond and give you specifics.

This post was edited by LizinElizabeth on Sat, Nov 1, 14 at 10:41

Thank you, LiznElizabeth for your kind reply. Mine are the herbaceous type you described, so I will cut them back. I just didn't know how much to cut back. Thanks again.