Here are two interesting articles about using blindfolds to wash your child’s hair
http://www.juniormagazine.co.uk/health/how-to-wash-your-childs-hair/12653.html
http://ot4specialtots.blogspot.com/2009/09/washing-kids-hair-who-has-tactile.html
The reason you may want to use a face washer to blindfold your child while washing their hair is to stop water getting into their eyes. Goggles could also work as the eyes are not covered in this case to prevent sight.
This could be a great way to introduce blindfolds to children where peeking is not the end of the world because the point is not the inability to see. If you hold a folded cloth over eyes, which is not tied at the back, it can be removed easily.
But the articles above are not how I discovered this idea. My own grandmother, who was a great lady, used to blindfold my brother and I while rinsing our hair.
Folded face wash cloths folded can make good blindfolds, as they are dark and thick and if the child does not need to use their hands they can hold it untied and better control their sight.