arrector pilori muscles which attach to every hair follicle in the skin contract the muscles generate heat in an effort to warm the body. the contraction is morecreates goosebumps on the skin. On the nipples it causes the skin to pull because obviously skin there is different somewhat.
unqualified theory: blood goes out to your extremities when you get cold (including your nipples.) but unlike your fingers, say, your nipples are full of erectile tissue that stands up when full of blood.
Because they are excited. Nipples were created to perform a particular task and are programmed to deliver when stimulated. They then protrude to enable the baby to latch on and feed. If they didn't, how the heck would the child find it's food?
Nipples get hard in the cold for pretty much the same reason that you get goosebumps. The nerves in the skin sense that it’s cold so they contract to reduce overall surface area and thereby conserve heat.