Do they even make hard rubber winter snow tires anymore? Since they switched to everyone insists on driving a vehicle capable of 200MPH, the rubber for tires has to be made soft, sticky. So you could have a tire that *looked* like snow tread, but it has summer "high performance hot rod" composition rubber.
I don't know the answer to that question either, but that is my guess if you can't find snowtires that work. Used to be everyone had two sets, summer, then winter tires with deep hard snow tread, I remember I always did, so did my dad, neighbors, friends, friends dad's, etc, at least for the rear drive wheels. People don't do that anymore up north? It was quite common back in the 70s when I lived in Maine.
"All season" just sounds silly on the face of it, like a marketing gimmick. The road surface and driving conditions vary a lot, I can't see where a "one size fits nothing exactly" style tire/tread and rubber composition would work very well.
It's like down here, you either buy *real* mud tires and put up with them on hard surface driving (and are smart enough to not try and use them on ice or snow, 4wd or not), or you get a poser mud tire "all season" joke look alike tire, that will leave you waiting for the dude with the winch to come by. Right now, that's all I have on my project truck, mud tire look similar wannabes, and I know the difference. Eventually a diff set of rims with real mudders on them, as the bulk of this truck's work will be offroad, not "offroad two hours on the weekends, and have to commute on hard surface anytime besides that".
So, I dunno man..hit the junkyard, get you another set of rims,(stock, steel, cheap, etc) get whatever passes for a real snow tire now for the winter, swap back and forth with the seasons and be done with it.