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OK, so here's what is going on. All the clues were in your description of the problem. Very slick road conditions, stop and go at creeping speed & an Auto tranny.
If you leave the tranny in Drive and try to come to a gentle stop in these conditions, a rear wheel drive car will do exactly what you experienced.
The front wheels will stop and one rear wheel will stop, but because the tranny is in first gear, the engine will overpower the one rear brake and it will continue to rotate (unless you really stand on it) causing the rear of the car to squirm or even head for the ditch.
The solution is easy, bump it into neutral just before you come to a stop when you are driving in these conditions.
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