Goosebumps, also called goose pimples or chicken skin*, are caused by the contraction of tiny muscles called arrectores pilorum. Fur-covered animals flex these muscles when they're cold to expand their coats to hold in more warm air, or when they're scared to look bigger and more threatening to predators. While we no longer have thick fur, we've retained these muscles throughout most of our bodies.
You have tiny hairs over most of your body, which are mostly connected to arrectores pilorum. However, the palms of your hands and the soles of your feet are hairless. These surfaces must remain flat when threatened to retain their gripping ability.
Your face still has arrectores pilorum muscles, but these have been adapted to a new purpose: facial expression. These muscles aren't attached to hair, and they're voluntarily controlled. This means they won't react in the same was as the muscles on your arms and legs when cold.
*In the 1940s and 50s it was common, if a bit rude, to call a woman in a short skirt "chicken legs" because her legs would be covered in goosebumps.
Posted 1618 day ago