I understand that the snow isn't nearly as bad in Plymouth as it is up here, but yes you are right incompetent driving causes most of the problems. I managed last years drive up to the Brecons in the snow just fine on Eagle F1s, but a lot of the downhills were basically a controlled slide and if I were to meet someone coming the other way we'd likely be looking at a crash.
In this sort of whether I'd suggest that you always give way to the guy who is coming downhill!
That said I'd still recommend the Nokians. The difference truly is amazing, being able to do a 3 point turn in a snow filled layby vs having to get out and push the front end about makes the trip so much nicer.
Yea, we've got about 2-3cm down here which really isnt that much. It's mostly gone from the main roads but the minor roads are still packed snow so I took the opportunity to get out there and get some experience. I got up a hill as well with the right amont of throttle though it did try and break sideways at one point

I was quite impressed really - it was quite easy to see how people would get into difficulty but also quite fun to test the recommended ways of avoiding problems, and finding they worked.