Condensation is your biggest enemy. You can buy dehimidifier crystals for unventilated lockers, or keep the doors open all winter (depending on their style), or line them with styrofoam sheets or that silvered bubblewrap (Home Depot). You shouldn't have anything in cardboard anyway, but that goes double in winter. Open the hatch in the head after taking a shower for a minute or so, no matter how cold it is. Try to keep air moving (we run the fan from our a/c even when we're using the space heaters, just to improve airflow.
Buy yourself a pair of "Yaktrax" ice cleats from an ourdoor store like REI or EMS (approx $20) for use when the dock is icy. Buy two pairs and keep one in the car for when you get home to an icy dock, and another aboard.