An interesting hat will have ribbons, lace, ribbon roses, feathers and other trim applied. Some doll makers dye all their trim items to match or get the color they need for the costume they have made. You can dye cotton, silk and other natural fibers and feathers with Rit dye (the same dye used to color bleached Tibetan Lamb fur for doll hair).
Follow this link to find a color mixing chart: http://teacupmilliner.com/design/mixing-rit-dyes-tutorial/
Color Formula Guide from Rit: http://www.ritdye.com/colorit_color_formula_guide
And a little DIY advice about dyeing fabric: