I made a game that had different hats the player needed to pick up to proceed, each hat gave a different skill. The way I did it was to place the sprite for the hat on the player sprite, then PIN it.
You could do the same here, have different sprites for different hair colour and depending on which one they choose, PIN that to the player sprite.
Either that or have the head, body and legs as separate sprite with different hair colours, tops and pants as a different frame of the animation. Then, set the frame for each part of the body and PIN the body parts together.