코끝이 시리다: The tip of my nose is freezing.

코끝: the tip of your nose, the end of your nose

시리다: cold, freezing

Ex) 귀가 시리다: My ears are freezing, 손이 시리다: My hands are freezing

→ The tip of your nose is directly exposed to the cold air during winter. Also, you keep on breathing in cold air with your nose, so it becomes cold, causing you to get a cold, or a freezing nose. When we say, 코가 시리게 춥다, it means it’s really cold outside.