Here on planet Earth?

Colder than a witches tit.
When the temperature falls low enough to freeze mercury in the bulb or t i t of a weather witch or what is commonly known as a mercury thermomoter it is said
to be as cold as a witches tit.

Exactly how cold would that be?

The melting point of mercury is -38.83 °C (-37.89 °F). While that's not an unheard of temperature, I'm sure most of us would agree that it was indeed colder than a witch's t i t long before that. RRC

Especially so in a brass brassiere

See, that's where I become confused again. I have heard "colder than a witch's t i t in a brass brassiere," but I'm at a loss to know why someone would put the bulb of a mercury thermometer in a brassiere of any kind in the first place.

I had always assume the phrase referred to the 17th-century belief that witches had an extra with which to suckle their familiars (part of the ritual of witch-detecting involved locating this teat) which was unnaturally cold. But I have never heard a thermometer called a "weather witch". Does anyone else know this usage?