Old English cūslyppe literally meant cow dung. Its components were cow and a word for paste. Middle English cowslyppe continued it.
The scored second component is paste; cow dung is the meaning of the whole compound. The source does not explain why that name was applied to the plant.
Sources
- Merriam-Webster: cowslip
Old English cū means cow and slyppe means paste; cūslyppe as a whole is glossed cow dung.
- Online Etymology Dictionary: cow
Also built on *cow* (Old English *cu*): cowbell, cowboy
- Online Etymology Dictionary · cowslip
Meanings of the older forms on the word path.