Two senses run together. 凛冽 is biting cold; 凛然 and 威风凛凛 describe an awe-inspiring, severe dignity. The chill and the sternness share one image: something that makes you shiver.
Left ice radical, the indexing component, two strokes picturing frozen water. It fixes the cold core of 凛, from which the figurative 'chilling severity' grows. Same ice family as 冷 and 冻.
Right 禀 supplies the sound — bǐng drifting to lǐn. It contributes no meaning here; it is a tall phonetic stack filling the right side of the character.
