The correct option is A even if it starts snowing
An adverb clause is a group of words containing a subject and a verb,
and it functions as an adverb, by modifying an adjective, verb or an
adverb. Adverb clauses generally begin with a subordinate conjunction
(since, because, while, etc.).
Option A is correct because it is an
adverb clause of concession or contrast, 'even if' is a subordinate
conjunction that refers to two ideas that contrast each other: "go to
the mountain top", "starts snowing".
Option B is incorrect because it
is a coordinate/independent clause, 'still' is an adversative
conjunction whereas an adverb clause is not independent. (Generally,
adverb clauses are subordinate/dependent clauses, they form a part of a
complex sentence.)
Option C is incorrect because even though it
is a subordinate clause, it is not relevant in meaning here, 'however'
means 'regardless of how', whereas 'even if' means 'no matter what'. The
latter provides complete meaning to the sentence.
Option D is incorrect because the answer lies in A.