From my Siberian childhood experience:
1. Take off your wet clothes immediately, put shoes back on though.
2. Run around and swing your arms to warm up and to dry out (don't forget to wring and dry your long hair too if any );
3. Put on your bag when the skin is dry (poncho style is the best, but if the bag is large enough - don't cut the top use it as a tent for now, breathe inside).
4. Wring out or press your clothes vigorously (I've been jumping on mine at the stage 2 above).
5. Put them on, bag on top (cut the face opening now), and then take care of the fire, or run for shelter.