There are three types of peony... let’s see what you do with them in the spring.
1) The old-fashioned herbaceous peonies which we associate with grandma require no pruning in the spring. Or anytime, for that matter. They do need to be cut down to about 4" in the fall and those stems and leaves should never be put in your compost because of disease. Municipal composting is supposed to be carefully controlled so it is hot enough to kill pathogens, although not so hot as to kill the beneficial microbes, so put them in your green bin or yard waste bag. Buds of herbaceous peonies are protected underground during the winter, and actually require a certain number of cold days to set buds, so no mollycoddling for them! For a new peony root, plant their eyes about two inches below soil level in the fall (best time to plant them) and they will just come back year after year.
Come spring, the only jobs are to put down some garden compost away from the emerging stems, and stake (or cut and bring into the house) the large doubles, which were bred to be cut flowers, anyway. Cut when bud feels like a marshmallow and leave enough leaves on the plant so it can feed itself. Cut no more than 1/3 of stems, maximum, leave 2/3. And cut just a stem long enough for your vase, and not at ground level. Ouff, sorry! That sound like a lot of work, but it's not...
Herbaceous peonies emerge from the ground in early spring, whence their protected buds have been hiding all winter! They come in all different colours and shapes of buds and unfurling leaves.
2 ) Tree peonies. When I first grew tree peonies, we had to protect them with stakes and burlap, and if they were planted in a spot which was even a bit windy in the winter, the flower buds which developed up to the top of the stems were almost always unable to withstand the cold. Climate change has made this covering of tree peonies a thing of the past. I now never cover them, only lose a couple of buds on the woody stems to cold, and often have ample buds coming from low down on the stems which produce flowers that same summer. Be patient and watch the topmost buds. When they begin to swell, cut back the woody stem just above the highest live bud on each stem. This is all it takes to make that tree peony look neat and tidy in your spring garden.
If your tree peony gets too big for its space, you can always give it a bit of a pruning in the fall, taking out any very old woody stems with few or no buds, and also removing any small, weak ones. Leave enough stems so they have a pleasing structure and can produce food through their leaves during the summer.
Tree peonies in spring…how to prune
3) Itoh hybrids have the best traits of herbaceous and tree peonies, from which they were crossed. They hold their next years buds near the base of the plant in the fall, so cut them back to the highest buds you can see on each stem. Then you will often find a few buds which have come through winter several inches up the stem. Do not cut them back to the ground, either in the fall or the spring, but do prune away the dead wood above the live buds come spring. It takes them a bit of time to get going at the beginning of the year, so be patient. Eventually, the live buds will swell and start to unfurl, while the dry-looking ones will not. Just take off the dead wood above an opening bud.
Itoh Peonies have buds like both their herbaceous and tree peony parents…some a few inches below te soil, some alive above the soil level through the winter, so do not remove them. Just take off the dead wood above the swelling buds.
As for all peonies, they can do with a bit of well-aged manure or garden compost either in the spring or fall, but be sure to keep it away from the stems. And, while peonies are pretty drought resistant, a dry spring like the one we are having now is tough on all plants in your garden. Give them a good drink to keep them happy. Your birds would love a bath in a sprinkler as well!!!
For all other peony related tasks - purchase, planting, dividing - please do them in the fall. You will have a happier plant if you do!!