coolness vs coldness

coolness and coldness both are nouns.

Word	Noun	Adjective	Verb	Adverb
coolness	Yes	No	No	No
coldness	Yes	No	No	No

As nouns, coldness is a hypernym of coolness; that is, coldness is a word with a broader meaning than coolness:

Other hypernyms of coolness include cold, frigidity, frigidness, low temperature.

As nouns, coolness and coldness are synonyms defined as:

Other synonyms of coolness include chilliness, frigidity, frigidness, iciness.

coolness (noun)	coldness (noun)
the property of being moderately cold	the absence of heat
a lack of affection or enthusiasm	a lack of affection or enthusiasm
fearless self-possession in the face of danger	the sensation produced by low temperatures
calm and unruffled self-assurance