False hair in dreams equates to false people you might be encountering in the walk of life.  According to spirituality, it denotes fake people around you.
According to Freud, dreams are based on the images we see in our day to day lives. It could also mean that you have seen someone wearing hair extensions or a wig, which resulted in such a dream.
Seeing false hair on your own head can indicate a situation where you will be tempted into sexual advances made by someone.