I wear a Black Diamond Tracer climbing helmet most of the time on firm snow days; my wife wears a Camp for descents on hard snow and in trees.
I wear the helmet for many reasons; the first and foremost is that it is the coolingest headgear I can wear that gives sun protection--even so, I often wear a sweat band underneath. I'll wear hats when the snow is deep, the weather bad, and the temps really cold.
I wear the helmet on the way up; I often ski on hard, icy snow; I often use ski crampons; and I use self-arrest grips under challenging conditions also; slides are almost always a risk when I'm skiing on firm snow (going up or down); I value my brains.
In tree skiing under sketchy conditions helmets provide some protection not only from tree boles but from tree limbs; the Tracer has webbing that prevent tree limbs from going thru the air vents on the sides. I don't like sun coming in from behind my sunglasses and the climbing helmet is just think enough to prevent that. Even short bill caps capture heat & moisture from my face and neck and can fog glasses.
So there are many good reasons to wear a helmet (just like alpine skiing, bicycling, etc) and only one reason not to--they look kind of dumb
Here I just skied a few hundred vertical of rough, icy snow, and after starting down a gulley that is usually fun, I found it excessively narrow, with hard frozen ski, boot, and snowshoe tracks, emerging tree tops, and debris, so I packed my skis and kicked steps down to a flat to eat lunch.