I have heard of exterior door handles freezing on earlier MINIs 2001-2004 (this can cause your problem), 2004-Present MINIs have a slightly updated exterior handle (which is supposed to stop them freezing), I would have thought in a country with a lot of frost & snow, these would have been changed on warranty at sometime

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I have also known this happen on UK MINIs when the door lock mechanism has failed / broken and the frost wont help either

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This happens on UK cars without the frost (the window stays put (doesn't drop a little))

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