Adjectives are descriptive words that modify nouns. A clause is more than on word. Reading through the sentence, Arctic is an adjective, but it is not a clause. A clause can also be set apart from the rest of the sentence (or be removed) and still make sense. In this case, if you removed, "where winters are long and cold", the sentence still makes sense, and this is a clause as it contains a subject (winter) and verb (are) and is describing the noun "region".
