cold, strict, severe
凜 centers on an intense, penetrating quality that can be physical or behavioral: biting cold, or a stern, severe demeanor that feels as unyielding as frost.
凜 combines the ice radical 冫 with 稟, which likely contributes the sound and the idea of something severe or imposing. The exact historical development of 稟 within this character is uncertain.
The ice radical 冫 on the left sets a freezing tone. The right side 稟 looks like a storehouse (亠 over 回 with 禾 inside), suggesting a cold, strict storage where nothing soft gets in. Picture a severe winter guard standing by an icehouse.
For リン, imagine a strict ring of ice forming around the storehouse: ring -> リン, and the cold, severe ring keeps everything frozen and rigid.