Why do you get cold chills when you poop?
Not medical advice: While having a bowel movement, your body is practicing self defense on a base level by making you look bigger while in an exposed position. Cold chills/goose bumps are an involuntary reflex started by the sympathetic nervous system, to mobilize the body's nervous system fight-or-flight response.
The sympathetic nervous system causes some muscles to contract and hair follicles to protrude outwards from the skin as a reaction to fear. The reflex of producing goose bumps is known as piloerection, horripilation, or the pilomotor reflex and can puff up mammals, thus, making a frightened animal seem impressive.
Passing a bowel movement is an intricate, coordinated event that requires a specific sequence of nerves and muscles firing. One phase of the bowel movement is the sympathetic phase and brief chills immediately after a BM is completely normal.