Most standard ski helmets are to warm to skin uphill in, except for the most bitter cold days.
That is a bigger issue than weight, to begin with.
Once it’s in your pack, it is just part of total pack weight, so whether you save 100g off your helmet, your backpack, your Waterbottle or what ever else, is all the same.
Of course, for a truly lightweight set up, you need to optimize every single item you are carrying uphill.
On my head, lighter is certainly nicer, but I find it less of an issue than on the bike, because you’re more upright.
For resort skinning I often wear my bike helmet. Light, and well vented, so it stays on for the up and the down. That saves time on our short laps.
For ski mountaineering, rock and ice fall is a worry, so a climbing certified helmet is Nice.
Among the dual certified helmets, Salomon Mtn Lab is 395g list, Dynafit ST is listed at 350g. Both have covered liners for your ears. Movement 3T is similar.
After that, there are some lighter helmets without that, but you have to include the weight of an extra hat then. Most of the lighter helmets are not ski rated either.
I bought the ST, but didn’t fit, so sold it to a friend.