As women grow older, they commonly sprout a few whiskers, and it is a perfectly normal part of aging.
Nose, ear and chin hair is dependent on male hormones, or androgens, which both men and women have. But with age, hormone levels change.
As women grow older, their estrogen levels drop, which means that there is less estrogen there to counter the effects of male hormones, which produces more hair growth.
It's nothing to be alarmed about and, if bothersome, can be treated with various forms of hair removal.