I NEVER assume tire dealers (or almost anybody else for that matter) have any idea what they're talking about. I always look for a second, third, fourth opinion... Yeah, some people hate me, but it's served me well. You'd think the "professionals" would know exactly what they're talking about, but they often don't. Anyway...
I noticed the same thing you did about the winter traction, and at first I was bummed when I ended up with the S/T-C's by accident since I use them in the winter. But, after driving in the winter with them, they left me wanting for nothing. They're like any "All-season" on hard cold ice, they're awesome in the snow, and pretty good on warm soft ice. I never had any problem on cold dry pavement either, though I do drive this truck prudently anyway. If I had this rubber on a car, maybe I'd notice more of a difference.
There are a few more things going on than just "hard and soft" rubber. Good modern winter tires have a "silica" rubber compound. It's not that they're absolutely softer, but rather than they do not stiffen up as much as regular rubber compound when the temperature drops. I'm not sure what the disadvantage to silica is, and why they don't put it in all tires. My guess is just cost, which is borne out by the fact that cheap winter tires don't have silica rubber, which is why they suck even though they are winter tires.
Similarly, there are certain rubber compounds that just hold up better to high temperature and high stress. Lots of guys go to trackdays with expensive high performance street tires because they say they "can't afford" racing tires, or don't want to bother with a change over. They go out, and chunk and completely destroy a $1200 set of rubber in one day. I use R-compound tires because I believe "different horses for different courses" and it's served me well. I get many many track days out of my tires if I'm careful. The rubber is soft, but I don't think that's really it.
I use Toyo RA-1's, which are a hard R-compound. Many other people use super soft ultra high performance street tires which are probably just as soft as my R-compound, but don't last nearly as long under the stress of track use. Even though the durometer is similar, the street tires chunk anyway.