Picture a length of cloth being laid over a body until nothing is left uncovered. That single movement — cloth going on, from outside, all the way over — is what the whole word is made of. Ask who holds the cloth and you get one branch of the word; ask what is under it and you get the other.
Wiktionary traces clothe to Middle English clothen and Old English *clāþian, the verb built on the same root as the noun cloth, from Proto-Germanic *klaiþōną. The material comes first and the action is named after it, which is why the picture inside the verb is always a piece of cloth going over something.
維基詞典把 clothe 追到中古英文 clothen、古英文 *clāþian，字根和名詞 cloth（布）相同，再往上是原始日耳曼語 *klaiþōną。先有布這個材料，動作才照著它命名。這就是為什麼這個動詞裡永遠有「一塊布覆上去」的畫面，也是它後來能拿來講草覆山坡、霧罩山谷的原因。
Wiktionary, entry 'clothe' (packet source_ref kaikki:3f6f69a190036ae4:928537061): 'From Middle English clothen, from Old English *clāþian, from Proto-Germanic *klaiþōną... See also cloth, clad.'
Two branches
衣服到身上：穿上，以及讓人有得穿
這一支就是核心畫面本身，只是站的位置不同：一個看的是布已經在身上的樣子，一個看的是布是誰準備來的。
verb · B2
To put clothes on a person's body, or to have clothes on. It is a formal or written word, and it appears most often in the passive: be clothed in something, or fully, partly or lightly clothed.
給…穿上衣服
像衣服一樣蓋住別的東西
同樣是「從外面整個覆上來」，只是身體換成了山坡、山谷，甚至換成一個人的職權或一個想法。
verb · C1
To cover something all over, the way clothes cover a body — used of grass, snow, trees or mist on a piece of land. The same picture is also used when someone is given power, or when a thought is put into particular words.
覆蓋；披上
以下是外部詞典記錄的用法，原文照列，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
clotheverb/ˈkləʊð/
To adorn or cover with clothing; to dress; to supply clothes or clothing.
To cover or invest, as if with a garment.
資料來源：英文維基詞典 English Wiktionary（CC BY-SA 4.0）。 原文照列，未經改寫。