The flowers of a tree peony are on new growth. You can prune to encourage limb grorth and branching by selectivly pruning the new growth after bloom.

Part of the attraction of tree peonies is the look of the woody growth. Especially in winter. Different types have different bark. Some as they grow develop ridges in the bark, others the bark has different shading between the newer and old bark.

I have many tree peonies and they definitely bloom on old wood. I never cut the woody stems unless I am cutting them back to where there was winter damage. The two oldest tree peonies I have bloom profusely every year on old wood.

Do you know which varities you have?

Most of mine send out new shoots from which the blooms come from. The new shoots should contain the bloom portion and segments of stem with leaves. You can direct the growth by cutting an inch or so above the leaf node. If the leaf is on the right side of the plant and you want it to grow in that direction cut above that leaf. If you want it to grow in a different direction select another leaf on the side that you wish the plant to grow and cut above it. Next year's growth will come from the inside base of the leaf. As the season advances you will see a bud like structure forming between the leaf and the stem. This is a future stem. Not all stems have flowers but most will.

You can cut the old wood but it may never recover or the cutting might force the plant to send out a new shoot.

One of the saddest things I have seen was at a house I toured in Oregon that had huge tree peonies that had been planted about 100 years ago. I returned several years later and some fool to paint the metal fence had cut the plants to about 8 inches above the soil. One lone small branch had grown from the twisted mass of old stems. A very sad relic of a proud plant. Mass was about 8 inches accross.

Uh oh! Now you're asking me the tough question! LOL!
I started collecting tree peonies from various and sundry nurseries, generally when I found them under $50. They were all just suffruticosa (as far as I now), and I'm not sure that is what you are asking. I am pretty bad with keeping track of the names as I'm not a hard-core collector. I just happen to like them and find myself buying them when I see one (a color) that I know I don't already have. I definitely have High Noon, Kinkaku and Rimpoh if that helps. Also have a basic no-named white one and several others that I really can't remember and didn't keep track of, but I'm sure had names.

Maybe what I am calling old wood is not what you are calling old wood? If I have a tree peony that has 10 old stems, that is what I mean by the old wood and I don't cut that back to the ground. A lot of growth comes off that "old wood". Then I also get new shoots in the spring from the base of the plant, which is what I am calling new wood. Are you talking about new wood coming off the old wood? Who's on first??!?! LOL!

Last winter there was severe damage to one of my larger ones. It was about 3'h x 5-6' wide. When the snow melted I found that most of the inner stems were snapped to the ground. I was very nervous about this since I had never cut them back before. I was so happy when about 10 new shoots came up from the middle. I can't seem to remember if I got blooms off those new stems.

That is really a shame about those old tree peonies. Mine are only 5-10 years old and I would cry for days if I lost even one of them.

We are talking about the same wood. This year look at the stems and you will see what I am talking about.

I was asking for the names like High Noon etc. If the leaves are more pointed they will have lutea in their background. Most are actually a combination over the centuries of Lutea and suffruticosa.

If you ever have breakage like that again try sticking the stems in the soil. I still have part of one that a deer stepped on and broke of part of the plant. I stuck it in the soil a few feet away and it survived and has bloomed once. However the bloom was not the same as the parent's bloom. The bloom was the same peach color but was interspursed with white edged green petals. The bud is too small to open this year so I will have to wait to see if the difference is permanent.

That is great info about breakage. I will absolutely try it next time. Not too much winter damager this year.