I’ve hiked the Pacific Crest Trail in this area... it cannot be emphasized enough- these are the big mountains. Winter is absolutely no joke and carrying an ice axe in your hands, and wearing crampons on the soles of your footwear is essential. Knowing how to use an ice axe is especially important. Anything else is folly.
You are correct and even with all the right equipment and ability things can go bad and the mountains don’t care whether you live or die.
My ice axe saved me from a long fall, First and only time I had to use it but it worked just like they said. And, yes, it was in the 60’s
Thanks for specifying where they should be worn.
Some folks here might otherwise think that they should strap them to their faces - which wouldn't help much.
Regards,