I would say that страшно is actually a short-form neuter adjective, rather than an adverb. (Mind you, for any given adjective, the neuter short-form is usually identical to the adverbial form, so they're only distinguishable by function: if страшно is modifying a verb, then it's an adverb; but if it's the predicate of a subject noun or pronoun, then it's a short-form adjective.)