noun, noun which may take the genitive case particle 'no'
the coldest season; midwinter
A formal, literary expression used in seasonal greetings or weather descriptions, referring to the period of severe cold.
In this coldest season, I trust you are all doing well.
As we enter the coldest season, please take care of your health.
酷寒 means 'severe cold' and can be used more broadly, whereas 厳寒の候 specifically refers to the seasonal period.
Compound of 厳寒 (severe cold) + の (possessive particle) + 候 (season, weather). The expression is a set phrase used in formal writing and seasonal greetings.