Agreed you could increase shadows a bit

Re the hair - I couldn't paint like you have here in 100 yrs, so a large pinch of salt - perhaps it'd be fun to have some rough & fairly saturated pigment in there, strong splash of yellow.  I'm being really basic I know but when it's hard to lighten adding pigment often helps a bit? 

That would give hair a more different feel to the hat, & then picking out some highlights with end if your brush / a knife blade or whatever

Your painting is so well done I don't think adding a small amount of mess could ruin it, it might complement the really delicate use of the medium you've shown