How cold is a very cold place? A tree peony, even in dormancy always has above the ground growth, like roses, which may need winter protection of some sort. Are you suggesting keeping your tree peony as a container plant? I would normally prefer to leave it in the ground, if this is a new plant now in a container, I would try and find a protected location for the winter and plant it in the spring. Al

thanks for the suggestion calistoga, my place is in zone 5. right now the temperature outside is 30f, snowing. it is going to be much colder for the next 3 monthes and we sometimes have snow in May.
it is a new bare root plant. i put it in a pot and hided it in my garage for 3 weeks already.
last year i planted 2 bare root tree peony early november, leaving them in the coldness. they all died in the following spring after a few weeks of struggling.
the new leaves start showing but the growth slowed, then stopped and died eventually. tears!