Cooper makes plenty of E load rated dedicated snow/ice tires.
While snow tires also generally have a softer rubber compound, the big thing they have is a lot of sipes in the tread, from the factory, though. That's why siping pretty much any other tire improves traction. Although I wouldn't want to sipe a tire that already has a fair amount of factory siping like most all season or highway tires. Don't want to slice up the tread into too many small slices either or they'll chunk out pieces of tread more and wear quicker.
Probably don't see Sumitomo much becasue they're, IMO, considered "cheap" tires. I've never run them and can't comment personally, but that's why.
They may be fine tires though.