Jīntiān xiǎo xiàyǔ.
False: 今天小下雨。
Jīntiān xià xiáoyǔ.
True: 今天下小雨。
形容词“小”主要作定语。误用作状语的“小”应移到谓语动词“下”的后边。“小雨”指雨量不大的雨。
The main function of adjective 小 is to be an attributive. 小 which is used wrongly here as an adverbial adjunct should be shifted backwards after the predicate verb 下. 小雨 means "a light rain".