The correct answer to what kind of word is the hyphenated word is 3. a compound adjective.
The hyphenated word is a compound adjective. It comes after the verb to be, which is a linking verb, modifying or specifying the noun "dreams". The dreams in the sentence would be stiff and frozen at the same time (also, stiff because they are frozen), so, "stiff-frozen". That expresses the dreams' characteristic, therefore, it consists of a compound adjective.
The correct answer couldn't be 1. a compound verb, because "stiff-frozen" doesn't consist in an action, thus, it can't be considered a verb. It expresses a characteristic, that's why it is an adjective.
The correct answer couldn't be 2. a compound noun, because it doesn't consist of people, place or thing. It is a characteristic, hence, a compound adjective.
The correct answer couldn't be 4. a compound adverb, because "stiff-frozen" isn't modifying a verb, but a noun, and therefore it can be understood as an adjective and not an adverb.