Green’s Dictionary of Slang

cold as... adj.

see also under colder than... adj.

In phrases

...a polar bear’s behind (also ...backside, cold as a dog’s nose, …an axe-head, ...a penguin’s behind, ...a snowball’s ass, ...polar-bear shit)

[1920s+] (US/Aus.) of temperature, extremely cold; also in fig. use.

...a grave-digger’s arse (also ...well-digger’s arse/ass)

[1950s+] (US) of temperature, extremely cold.

...a step-mother’s breath

1. [mid-late 19C] (US) of temperature, very cold.

2. [1920s+] (Aus./US, also cold as a grandmother’s/mother-in-law’s kiss) used fig. of a person’s emotions, very cold.

...a nun’s nasty (also cold as a nun’s crotch)

[1960s+] extremely cold, or sexually frigid.

...a witch’s tit (also cold as a witch’s behind, ...witch’s teat, ...witch’s titty, ...frog’s tit)

1. [1950s+] (also frigid as a witch’s tit) extremely cold, temperature wise.

2. [1950s+] completely without emotions.