Make the mulch covering about 6 inches deep. Remove the mulch in late February or early March. Fertilize with a rose type fertilizer in late February. Water thoroughly after application. Of course, apply according to label instructions.
Peonies are quite hardy, except for the tree types.
I loose several from rotting each year. I do keep them in an un-heated room, under the house. Handle with special care, so as not to bruise them. If the fruit has marks or bruises where it has touched the soil, use them right away. Leave the fruit on the vine until it is ripe.