First concept

one Idea I had was to make a foldable hat. one that could have a hard casing but in sections that then could be folded up, so that on a hot day you could take it off, fold it up and put it in your pocked but when wearing it you had more protection then a beanie,

i want to keep to the normal beanie look as posable so looked at the different common shapes. the first was the normal shape with the flappy ear parts to keep their ears warm and the folds would go down the center of the ear parts. the next I looked at the normal round one where the bottom rim is folded over, I felt if I did this one I would make that part elastic so it would hold on to the head better as I am scared that if the segments are hard then they wouldn't hold to the head as well so I would be scared the hat would fall off, so having the elastic part it would hold on but it would also be easy to fold.
My last idea I felt would fit my preference better, I enjoy skiing with only ear warmers (a headband type thing but sits tightly over the ears) i like skiing with ear warms as it means my head were the hair is can breath but my ears and forehead can stay warm, but in this idea it would have the segments but between them will be made of mesh so it can breath, the problem with this one is that on wet days the snow/rain could get inside the hat and defeat the purpose of it and make your head could and uncomfortable so would have to find a way to get air into it but keep it waterproof.

Sketch model;

I decided to try make a sketch model to see if my idea would work, I know the actual shape docent match a shape of the head but I wanted to see if you could get it to fold and it does fold in the way I want it to fold. but as your head is not cone shaped and rounds over, either the materials would have to be able to fold flat when not on the head or would have to be in segments that are curved when in the hat position so have tension on the fabric when like that so it sticks to the shape of the head and then flattens out and collapses when not on the head.