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The Ice Governess is a villain that appears in Doctor Who as one of the antagonists that appears in the Christmas special “The Snowmen”. She was the reincarnation of Francesca and Digby Latimer’s late governess who had died a year earlier, drowning in the frozen pond. The Ice Governess was animated on Christmas Eve 1892 by telepathic “snow” that embodied Francesca’s fears and nightmares about her late governess coming back to life to get her. The Great Intelligence wanted to use the Ice Governess as a template to produce an army to obliterate humanity and take over the Earth.
Once reanimated, the Governess attacked the Latimer family, but was thwarted by The Doctor. She then came back and learned not to melt. Thereafter, she seemed to have an obsession with saying “That’s the way to do it!”, mirroring the words of The Doctor while she was coming back. He managed to trick her into following him and Clara up the stairway leading to the TARDIS to keep her away from the Great Intelligence. The Governess managed to break into the TARDIS and take Clara with her, falling over the edge of the cloud it was on and shattering on impact (and killing Clara in the process). The Doctor took the remains and kept them in the TARDIS, where she could not reconstitute herself.
The remains of the Governess presumably remained stored in the TARDIS.