For years we have debated this: throw a shovel full of mulch over each plant or let them tuff it out? Steve in Baltimore County.
I usually mulch them some to keep any weeds seeds from germinating anyway in the middle of the plant/bush.
My newly planted ones may get some extra mulch, as the dirt has settled and the roots are exposed more then I would like. They'll get more soil if I get out there as I should and do it b4 all is frozen and useless.
Newly planted herbaceous always get a mulch for first
winter after that they fend for themselves. I currently
have 102 in my collection and have never lost one.
I do a walk in the early spring to check for heaving and
cover any that may be pushing a little too soon.
Instead of mulch on top of the plants - you might want to mix wood ashes (from fire place) and fall leaves and place them on top of the plant. Too much mulch might encourage rodents and diseases.
I use leaves to mulch my peonies, and I have had them for 10 years. I do cut back the stems in fall and this keeps them from getting mushy and diseased. Also remember that if you are splitting them at any time, they do not like that, and they will regress for about 2 seasons, then they will come back.
Here is a link that might be useful: home
In northern zones, there is no need to give special attention to peonies.
The big enemy is the freeze/thaw/freeze/thaw cycles that happen and cause the uplifting of the plant.
Usually though, no mulching is needed as long as you have reasonable snow cover.
But, in zone 7 Maryland, the mulching is not only recommended, its a must because of the milder winters where the upheaving is more likely.
Old hay/straw is I think a better mulch than wood chips which can put more dampness in contact with the crown.
But straw does pose a problem if mice might think to nest in it.
A ring of lime around the straw should deter that.
Lime of course, can be given peony....as wood ashes from a good source, can also. Wood ashes should be remembered to be watered in well in spring.