Right now, most self-driving software will refuse to activate in conditions of poor visibility. I've had that happen with Tesla's FSD, though in that case it was snowing so much that the road should have been closed. Also when the snow is deep enough that your front bumper becomes a plow, it will refuse to activate.
In ice none of these really stop overcorrection, or at least they don't in my 2020 truck on icy hill/mountain roads in Maine. And I've seen nice recent Volvos and BMWs with presumably the best safety tech in ditches up in the ski towns. The correct safe speed to drive on icy roads is not to drive at all of course, but people have to get places and people make mistakes. IME the assistive technology defaults don't do great on ice roads on some kind of up/down grade.
AFAIK drivers can still steer and brake themselves into a loss of control situation on ice regardless of safety features. So I guess I'm hoping once you take those two variables out of their hands, the FSD vehicles will be safer. Who knows though.
I went many years without a loss of control and the one time it did happen (logging roads with ice pack) was enough for me to buy Nokian studded winter tires to minimize the effect of ice as much as possible.
If a self-driving car does the right thing staying "in lane" while all the human drivers do the wrong thing flocking to new emergent paths (which swing back and forth across the "lanes"), then the self-driving car is wrong and dangerous. I'm not talking about when it's actively snowing either. I mean the snow on the ground just remaining there, covering things.
It's not about dealing with slippage or skill driving, it's about complete lack of context markers. I don't think any current or near future self-driving solution can adapt to this.