I, too, used to envision a cloak as having sleeves. Then a friend of mine burst my bubble with the following:
Main Entry: cloak
Pronunciation: \\klôk\\
Function: noun
Etymology: Middle English cloke, from Anglo-French cloque bell, cloak, from Medieval Latin clocca bell; from its shape
Date: 13th century
1: a loose outer garment, which differs from a robe in that it has no sleeves, but uses slots through which arms can protrude from inside the garment. The arm-slots also differentiate the cloak from a cape, along with the hood, which a cape does not possess.
I kept it to remind myself that I'm not as smart as I thunk I was ...
I'll shut up now ...