With age, the skin becomes thinner and less elastic due to a decline in connective tissue components collagen and elastin, and due to cross-linking of these proteins by molecules called advanced glycation end products. This makes the skin more fragile and results in the formation of wrinkles. Aged skin also takes longer to heal.
Anatomical Difference Between Young And Old Skin
Aging can result in hair loss, though this is far more significant in males, and can happen for different reasons. With age, individual hairs spend less time in their growth phase (see here for an explanation of how hair grows), and hair follicles become smaller and eventually die.
Hair also becomes grey with age. This is caused by the death of follicular melanocytes, the cells that produce the pigment responsible for hair colour.