What is the importance of the color pinkThe ribbons on faith's hat were pink. They are mentioned a few times and they are usually moving
Pink is often associated with innocence. Everyone in Brown's pre-forest adventure is viewed as innocent ... perhaps, to follow the color hint, through "rose colored glasses" --- at least in Brown's estimation. (Of course, when he comes out of the forest they haven't changed ... he/his view of them, have.) The ribbon is the physical symbol of innocence, and it appears later in the forest as it drifts down from above, suggesting that the woman that is going to be inducted in the forest ceremony is Brown's wife --- the loss of the pink ribbon would be the loss of her innocence. Of course, we don't know if any of this ever happens since it is suggested that this whole experience is a dream.
If it's real, then the pink/innocent ribbon would represent the loss of Brown's wife's innocence in fact ... but with Hawthorne's ambiguity we don't know if it happened. And it's not important. Brown is forever changed by what he thinks happened, and that's what's really important.