Just being plain cold outside isn't going to freeze up a starter unless it's full of water and I'm not sure how it would stay full - if the water can leak in, it can leak out also. Have been in the cold winter for 50+ years and never seen a starter freeze and I've been in it down to -67F.
I've plowed enough deep snow in the winter that I've filled up my air cleaner and killed the diesel engine, but I've never had a water or water & freezing problem with a starter. The snow is deep enough up in the hills so that I have to run with all four chained up with modified chains, a 1,000# of weight in the bed and locker units in the front and rear ends.
I've also flooded out my Jeeps in enough deep rivers where I have to use the electric winch to at least pull them far enough to get the spark plugs out of the water to get them restarted. Also sunk one in a river so far that the steering wheel was under water. Just water has never given me a starter problem.
I think you have other problems than cold weather and or water.
Bill