Comparatives and Equatives

When making a simile (as...[adjective or adverb]...as), is there a certain rule for some things?

ADJECTIVE modifies NOUNS: He is as clean as a whistle.
ADVERB modifies ADJECTIVES, ADVERBS, and VERBS: He runs as fast as the wind.

But what about NON-ACTION VERBS?

Ex: He looks as cold as winter itself. <- adjective
He can understand as quickly as Brad. <- adverb

Are there special cases for non-action verbs? Or is it just a few? Usually it seems that they would have to use adjectives to help modify them. Any help would be appreciated. Thank you.