Socks are considered to be under shoe wear since you wear the socks under your shoes.
Although most people do consider socks to be footwear which I myself do.
Anything you wear on your feet whether for looks or protection is footwear.
I like to lounge around the house or walk around the house wearing just my socks especially during the winter months.
Socks also keep my feet very warm and comfortable sleeping at night.
Socks also make your feet more comfortable when wearing shoes.
Footwear refers to garments worn on your feet, which serves to purpose of protection against adversities of the environment, usually regarding ground textures and temperature.