What is the name of the smooth muscle attached to hair that causes it to stand up when cold or frightened?

The smooth muscle that is attached to hair follicles and causes hair to stand up when a person is cold or frightened is called the arrector pili. This small muscle contracts in response to various stimuli, resulting in the hair standing erect, a phenomenon commonly known as "goosebumps." This reaction is part of the body's natural defense mechanism, serving to provide insulation by trapping air for warmth or making an organism appear larger to potential threats.

The other terms provided do not accurately describe this specific muscle. The sebaceous muscle does not exist; instead, there are sebaceous glands that secrete oil to keep hair and skin moisturized. The hair follicle refers to the structure from which hair grows, rather than a muscle. The term dermis muscle is not a recognized name in anatomy, as muscles are not specifically categorized in that manner within the dermal layer. Therefore, the arrector pili is the only correct term in this context.