Interestng to read the comment about the 1 Series in the snow. I wonder if part of the problem is the car being so light? My 435d has X-Drive and standard tyres and it's been surprisingly grippy and stable on the recent snow and ice - even on the hills of Sheffield and the higher stretches of the A68.

Possibly, though I suspect that it has more to do with:

1. The area that the OP lives is VERY rural/high up and thus roads are not gritted and probably suffer higher levels of snow, very low usage to even start to help clear the roads of snow, made even worse as they are probably not much better than farm tracks (C roads), and;
2. Their car has very low profile, wide tyres that have less weight for every mm2 of contact on the road than your larger beemer (probably not that much difference in tyre size, but, as you say, far less weight), plus;
3. The type of tyre each car is shod with. Yours may be also a summer tyre, but some seem to work better than others in wintery conditions, even if all summer tyres are ouclassed by a factor of 10 or more by all-season, and even more so by winter tyres in snow and icy conditions.

The guy is supposedly an 'advanced driver' not to mention a former saloon car racer but in icy conditions he considered having his foot 'hard down' on the brake pedal the best course of action? Nah, something amiss there.