Hair is a natural extension of the body. It is something that comes out of the body and something which in many ways can reflect the personality of the person that it is coming out of in a variety of different manners.
If you have a dream of dying hair it means that great changes are coming for you. You are going to need to put your best foot forward and accept these oncoming changes. The changing of hair through haircut or through dying hair means that you need to brace yourself for more changes in the near future, directly to the way that you live your life. This is an important dream symbol and it is what will carry you through in life. For clarification purposes, this meaning is related to dying hair in the sense of the act of having your hair dyed. This means that you are going out and having colors added to your hair to better reflect your personality and thoughts.
To dream that you have dying hair such as hair that is literally dying, going gray, or falling out, then this means that you feel like you are getting old. Perhaps you feel mature in the sense that your ideals have changed to reflect those of someone more mature in age and ideology. It is also possible though that your body is just aging and you are finally beginning to notice it. This is one other meaning of a dream about dying hair.