doesn’t the invisibility cloak render the wearer invisible? In which case when Hermoine is wearing it, no one can see her or her hair. the cloak is not only invisible, it makes you invisible too. its not like the point of the cloak was that u cudnt see it so people would be like, “its freezing outside and youre not wearing a cloak???” and you could smugly say “but I am friend, but I am” leaving your friend awestruck. its so that people CANT SEE YOU. and you can sneak around castles at night looking for mirrors of Erised. and obviously, so you can cover your hair without actually wearing a kerchief that will ruin your appearance, which becomes a non-issue anyway bc you no longer appear.
so yeh. not sure what that accomplishes but ok.