Plaster is a very thick material, but it's not a substitute for insulation. You'd need to find out if there is insulation in the walls and if not, try to add some. The easiest way with plaster is to do blown in insulation, where they drill a hole and then fill the cavity. It is a little more expensive than fiberglass, but won't involve all the work of drywalling over the plaster. This typically isn't DIY project, though, but perhaps get a few estimates and try to figure out if there is any insulation to begin with.
In terms of adding carpeting, I would make sure there are no moisture problems in the basement first. If you've been there awhile you probably know, but I'd want to check into at least adding a sump pump and/or drain tiles if there is a moisture problem. Otherwise the carpeting might get ruined with a big rain. Often you can keep water out by making sure your yard is draining away from the house and that the downspouts are funneling it away. Here's more on basement.