For instance, the kan'yōku kitsune no yomeiri (狐の嫁入り, literally 'a fox's wedding', meaning "a sunshower") and the yojijukugo koharubiyori (小春日和, literally 'small spring weather', meaning "Indian summer" – warm spring-like weather in early winter) are not proverbs.
To be considered a proverb, a word or phrase must express a common truth or wisdom; it cannot be a mere noun.
(I no naka no kawazu (井の中の蛙, 'a frog in a well') is Classical Chinese, from the Zhuangzi.)
For example, one might say i no naka no kawazu (井の中の蛙, 'a frog in a well') to refer to the proverb i no naka no kawazu, taikai o shirazu (井の中の蛙、大海を知らず, 'a frog in a well cannot conceive of the ocean').
Whereas proverbs in English are typically multi-worded phrases (e.g. "kill two birds with one stone"), Japanese yojijukugo borrow from Chinese and compactly convey the concept in one compound word (e.g., isseki nichō (一石二鳥, 'one stone two birds')).