that'll be the frosty Friday

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.

• (Received Pronunciation) IPA^(key): /ˌðætl̩ biː‿ðə ˌfɹɒsti ˈfɹaɪdeɪ/, /-di/
• (General American) IPA^(key): /ˌðætl̩ bi‿ðə ˌfɹɔsti ˈfɹaɪˌdeɪ/, /-ˈfɹɑsti-/, /-ˌdi/

• Audio (General American):

  (file)

• Rhymes: -aɪdeɪ, -aɪdi
• Hyphenation: that’ll be the frosty Fri‧day

that'll be the frosty Friday

1. (idiomatic, informal) Synonym of that'll be the day (“said in reply to something that one believes will never happen”)