The stoat's seasonal moult is triggered by day length rather than temperature. In autumn the brown summer coat is replaced by white, and in spring the reverse occurs. Throughout, the terminal third or so of the tail stays black. That persistent mark is the detail that heraldry borrowed for ermine fur, the white field studded with black.
Why keep a conspicuous black spot on an otherwise camouflaged animal is a real puzzle. The leading explanation is deflection: a hawk or owl aims at the highest-contrast point, and a black tail tip trailing behind a running stoat draws the strike to a survivable place. Field experiments using stoat models with and without the black tip have found more attacks directed at the tail end when it is present, which supports the idea without closing the question.
The same animal's behaviour has been badly mythologised. Reports of stoats mesmerising rabbits by dancing are common and old, and while stoats do perform erratic leaping bouts, the interpretation as deliberate hypnosis is not supported. One well-documented alternative is that the behaviour can be caused by a parasitic nematode infesting the nasal sinuses.