type of oak
栩 refers specifically to a type of oak tree, the kunugi (sawtooth oak). Its meaning is narrow and botanical, centered on this particular tree species.
栩 combines 木 (tree) with 羽 (feathers/wings), likely as a phono-semantic compound where 羽 hints at the sound and 木 indicates a type of tree. The exact historical development is uncertain.
A tree (木) with leaves shaped like feathers (羽) — picture the sawtooth oak's feathery foliage to remember it's a type of oak.
For ク, imagine a cool (クール) oak tree providing shade: cool -> ク, and the oak's feathery leaves rustle in the breeze.