The story
Probably a humorous elaboration of that’ll be the day, with frosty and Friday chosen for the alliteration; probably also implicitly evoking a cold day in Hell, referring to when Hell freezes over.
Etymology from Wiktionary, CC BY-SA 4.0.
that'll be the frosty Friday
that’ll be the frosty Fri·dayToday it means: Synonym of that'll be the day (“said in reply to something that one believes will never happen”). Full definition →