A couple of suggestions:
1. A locker is a really poor place to dry clothes. I hang mine in my cubicle and most days they are dry for the return trip.
2. When it cooler (and dry) you won't sweat as much and your clothes should not be as damp. I find during the winter my clothes are only wet after a drying period if it was raining.
3. Wool will be warmer when wet than synthetics. It will still be uncomfortable to put on but will warm up quickly.
4. Your base layer is probably going to be your only problem in the winter so you can just carry an extra set of shorts and base layer t-shirt.
Good luck and congratulations on becoming a winter commuter.
Craig