I typically wait too for the better temps of Spring. Most succulents by then are back to their active growing vigor. And it is easier to dry off and callus the plant and avoid cold damage. If there is an open wound or cut after you separate the pups , I carefully apply cinnamon on it for protection, it is a natural fungicide. Apply it on the open cut, avoid the roots. I also usually try to wait if possible for the pup to be at least half way the size of mommy, so it has good energy.But they are such slow growers so make sure your container to repot is not too deep or too big for it.
If my original container is wide enough, I just allow the succulent to make a nice colony there with its pups, they do make a nice specimen altogether..but if it is like yours, then I have to repot, they are getting too tight there.
