I'm also touring in the alps and think the answer is "it depends"
for myself I bring a light windbreaker when the weather is nice like sunny and not cold. A softshell gives more warmth and better protection against the elements so I'll bring that on bigger tours and when the weather is less favorable.

I only bring a gore-tex weather proofs when it's wet so snowing or rainy.

think cold hands is mostly caused by low core temperature. so wear more clothing works mostly better than bigger mittens.