Is that a lutea, right? In that case I wouldn't worry too much about the bark... but I would worry about that pruning job.
Lutea are tricky when it comes to pruning and in their first years are usually better left alone. It's customary to just remove dead and deformed growth while the plant gets established. In most areas this is done in late February/early March but in your area it's better delayed until the first buds start to grow to see what is sound and what needs to be removed. While snow in itself isn't bad (in fact it can help protect the plant from wind chill) it can snap stems.
So here's the question... why did you perform that surgery on that peony?
