And now how it looks in reality.
All you hair fibers above skin surface (that what you are supposed to collect for storage) are dead. there is no single living cell in your hair fiber.
All epithelial cells, that form hair fiber are produced by hair matrix at the base of hair follicle along side with inner root sheath. Both inner root sheath cells and hair fiber cells undergo well coordinated, programmed cell death, called apoptosis. Upon apoptosis special enzymes destroy all vital cell's proteins and intracellular compartments. All DNA within a cells also undergo destruction. Intact chromosomes are fragmented into millions of small pieces. It is well known phenomenon. It is even used in research. TUNEL, special technique helps to identify dead cells by detecting fragmented DNA. What is left after hair cells dye are keratinized, hard "shells" that serve only mechanical function.
So, by storing you hair fiber sample you are not storing useful DNA, you ares storing DNA junk.
Even more naive will be to hope that cells within your dead hair fibers can be used for hair cloning. For hair cloning one need alive cells! Only alive. And only cells with high morphogenic potential. That is - either stem cells from the hair bulge area or at least precursors cells at the based of hair matrix - clonogenic cells (these cells were recently described by Hair Follicle Predetermination hypothesis).
So in order to save your hope for cloning your hair in the future one need to cryopreserve alive hair follicle extracted from his head by micro-surgical.

please be aware of information above when deciding to store you hair fiber samples for $50 initial fee and $10 annual fee after that.