cold spell vs while

cold spell and while both are nouns.

Word	Noun	Adjective	Verb	Adverb
cold spell	Yes	No	No	No
while	Yes	No	No	No

As nouns, while is a hypernym of cold spell; that is, while is a word with a broader meaning than cold spell:

cold spell: a period of cold weather
while: a period of indeterminate length (usually short) marked by some action or condition

Other hypernyms of cold spell include patch, piece, spell.

cold spell (noun)	while (noun)
a period of cold weather	a period of indeterminate length (usually short) marked by some action or condition