I heard a friends say that he's going to take a small nap. Is this correct usage? I thought we only take light naps.
'Small' doesn't make sense here because the adjective referring to the length of time (duration) of a nap. Small is more of a descriptor for the overall size of something rather than length in particular (such as the saying, "it's a small world").
'Short' is better because it is an adjectives used to describe length (of time or of objects). You might say "that was a short drive" or "the dog is playing with a short stick."
'Quick' is also appropriate here because it is used to describe duration (length of time), such as "it was a quick meeting."
A 'light' nap is also correct, but it is not referring to the length of the nap. It is instead is stating that the nap does not involve a deep sleep, and typically that implies a shorter nap.
Edit: saying "light nap" is similar to "light snack". Snacks are smaller than a meal, but adding the modifier 'light' implies it's a smaller snack than usual, possibly with healthier or less filling food. A light nap might be 5 minutes of just closing your eyes and breathing deeply, barely even sleeping, as opposed to a 2-hour nap where you likely reach deep stages of sleep.