cold weather vs frost

cold weather and frost both are nouns.

Word	Noun	Adjective	Verb	Adverb
cold weather	Yes	No	No	No
frost	Yes	No	Yes	No

As nouns, frost is a hyponym of cold weather; that is, frost is a word with a more specific, narrower meaning than cold weather:

Other hyponyms of cold weather include freeze.

cold weather (noun)	frost (noun)
a period of unusually cold weather	weather cold enough to cause freezing
	the formation of frost or ice on a surface
	ice crystals forming a white deposit (especially on objects outside)

cold weather (verb)	frost (verb)
	damage by frost
	decorate with frosting
	provide with a rough or speckled surface or appearance
	cover with frost