우듬지 is a pure Korean word. The Chinese character meaning 우듬지 is 梢 (초), which is listed under the "tree" radical 木 (목) in Chinese character dictionaries. If you wanted to describe the sound of treetops rustling in the wind using Chinese characters, you would write 梢梢 (초초).
The human nervous system is divided into the central nervous system (중추신경계 中樞神經系) and the peripheral nervous system (말초신경계 末梢神經系). In the Korean name for the peripheral nervous system, the 말 in 말초 (末梢) means "end," so the word that Koreans use to mean "peripheral" (말초 末梢) literally means "the ends of the top branches of trees." Doesn't that make the Korean word for "peripheral" (말초) easier to remember?
The following is a video of treetops rustling in the wind (梢梢).