Translation:When it is cloudy, I like reading books at home.
If you're translating from English yes, absolutely; "I like reading" normally refers to books and can be translated "看书". But in Chinese the reading material is often specified (看书, 看杂志, 看报纸) so when translating Chinese to English, I'd also specify books, magazines, newspapers...
It seems that in the Chinese way of saying this, it is like saying "at the time of cloudy", but in the order of the words it is like "cloudy's time" where the "de" corresponds to the English apostophe s. With this construction you can say things like "when studying" or "when resting" which would be verb + de+ shihou. So, the expression "de shihou" should be learned as a unit that means "at the time of ..." Hope this helps.