A sounds right if someone who would ordinarily swim doesn't go in the water this time because s/he's too cold.
B sounds right if the person is already in the water when s/he realizes that it's too cold to swim. Although "It's / the water is so cold that I can't swim" might be more natural.
C would be a person giving two reasons for not going swimming, or maybe for not going to the beach/lake/pool.
Anna sounds right, but I would add that with C you sound as though you are making two unrelated observations despite their being in the same sentence. None are grammatically incorrect.
Comments
All are grammatically correct.
A sounds right if someone who would ordinarily swim doesn't go in the water this time because s/he's too cold.
B sounds right if the person is already in the water when s/he realizes that it's too cold to swim. Although "It's / the water is so cold that I can't swim" might be more natural.
C would be a person giving two reasons for not going swimming, or maybe for not going to the beach/lake/pool.
A. Sounds most natural, that's what I would say.
B. Suggests you are extremely cold, like hypothermic, and can't move.
C. Implies that you don't know how to swim.
Hope this helps.
To me, as a Briton, A seems the most natural, B sounds more formal. C is different, it puts forward two ideas that are not necessarily connected.
Anna sounds right, but I would add that with C you sound as though you are making two unrelated observations despite their being in the same sentence. None are grammatically incorrect.