Why do hair on your bodies stand out when you are cold?

It doesn't, it's just that the cold temperatures cause your skin to contract exposing the hair that you may have missed while shaving. To solve this probem, try not to shave in the shower or when you first wake up. Both of these will raise your body temperature and cause your skin to puff slightly and cover the hair a tiny bit. This small bit is enough to be noticable when the skin returns to normal exposing those tiny hairs.