If it's relatively warm (mid 50's or above), I just wear base layer top and nylon pants and get wet. At night, those wet clothes are in a 2 gal. ziplock bag in my sleeping bag. They don't get dry, but at least they are warm when I put them on in the morning, and the moisture isn't in the sleeping bag insulation. If you have troubles waking up in the morning, leave them out; you'll wake up in a hurry when you put them on!
If it's a bit colder, like now (mid-40's), just rain jacket and pants over base layer top will do. I often end up with the rain jacket open for more ventilation while I'm actively hiking.
If it's really cold (like 20's or below), I wear a lightweight fleece vest under the rain jacket.
The trick is to try to avoid sweating as much as possible. During rest stops, the puffy goes on under the rain jacket, being careful to keep it dry. Keeping stops short helps prevent chilling.
I have a dry baselayer top and bottoms, socks and puffy jacket for in camp and in the sleeping bag. Of course the rain jacket and pants go back on if I'm out in the rain! The only duplicate items are a second baselayer top and a second pair of socks. Actually, if I know up front it's going to be rainy the whole time, I may take a third pair of socks.
This article from the BPL archives (2006) is an excellent guide to staying comfortable in sustained cold, rainy weather:
(remove the space after "rain." when pasting)