Mulch isn't really necessary for peonies although they advise it to help avoid heaving soil. Has anyone here ever had heaving soil??? I mulch mine but only because it's so dry here in CO, would be watering daily if I didn't. I have mulch completely covering my peonies now, mostly just pine straw so it doesn't create such a solid barrier like wood mulch, but I move it back in the spring as soon as I see signs of growth.
