Gosh, she hadn't a clue, had she? I suppose she was in first gear too, with the wheels spinning like that! She probably had no idea whatsoever that the car is rear wheel driven. I spent about 7 years in my early driving life in the Peak District, where you just HAD to know how to get out of a fix. Always went to work with ballast in back, boot or van back, and a shovel, with a sack or two.
I've got an ancient 3 Series and it's not bad but I believe some of the new ones are hopeless in snow and ice. I do try to avoid it whenI can though and get a bus or walk unless I have to in these conditions.