The story
Probably an allusion to a situation being seen more clearly in daylight, and after some time has passed. The word cold is used in the sense of “dispassionate; not prejudiced or partisan; impartial”.
Etymology from Wiktionary, CC BY-SA 4.0.
in the cold light of day
Today it means: Viewed calmly and dispassionately after allowing emotions to cool or after having sobered up. Full definition →