What is the biological function of nose hair? In general, can we consider underarm hair and pubic hair to be vestigial structures?
From this article I quote
If you look on an evolutionary perspective, the arm pit hair follicles as well as pubic hair have a type of sweat gland associated with them, called an apocrine gland, that begins to function at puberty and is widely associated with scent-communication via chemicals known as pheromones (reference).
Some other functions that are associated with pubic hair are:
The nose hair is definitely not vestigial. As long as the armpit hair (between the body and arm in certain heavyset individuals) and pubic hair serve to reduce friction and male sweat serves to increase female hormones, I wouldn't call them vestigial (reference).