I'm a big fan of trekking poles. Haven't used them for much except with snowshoes or skis (with baskets), but they have prevented me from falling over a few times. My self-arrest training was on fairly steep snow in NZ with a big run off and after being shown what to do, we would basically toss ourselves down the hill and try to stop within a short distance. If the terrain is flatter, then not so much of a problem, obviously, but falling over with a big pack on, as I did a couple of times in Yosemite in soft snow on one trip, it was a real hassle to get back up, even with poles.

Even here in So Cal where it does get snow and ice in the mountains, there has been at least one accident where a hiker fell off a trail when she slipped on something-probably ice, but that was undetermined. Unfortunately, she was dead by the time SAR found her. I think she was training for a cross-country run, so she had no poles or traction devices on her shoes.