A, B - Incorrect: The modifying phrase that comes at the end of the sentence modifies the preceding nouns mukluk boots and parka hoods, which are the subjects of the sentence. The modifier a method does not make sense in describing the clothing items. Answer choice B incorrectly uses the preposition as, which implies that items of wear are a method.
D - Incorrect: Referring to parka hoods as a protection is very awkward.
E - Incorrect: Infinitives such as to protect should not be used directly after a comma.
C - Correct: The active participle protecting correctly modifies mukluk boots and parka hoods to convey what these clothing items do for the people of Prudhoe Bay.