Hello, Anna. I am brandy from China, suddenly I saw your question, and I am very glad to explain for you. 放牛吃草 is Chinese idiom whose metaphor is to give somebody enough freedom.

It doesn't mean "to set free" as in the English meaning. It means "to let it be". For example, an exasperated mother would console herself of a recalcitrant child, "let him be". This stems from when the shepard opened the pen, he does not have to worry about the cow. It simply lumbers off off to eat grass and do its own natural thing.

我太孤陋寡闻了，第一次听说还有这么个成语。

This is a China idiom, and China idiom usually doesn't only have one mean. You can see just the word mean or maybe have the deeper meaning. They need to see the sentence before and after to judgment this idiom that what it want to mean. So, the same idiom in the different sentence will be different mean. If you only see this idiom, but why this way is this mean and another way is another mean, you will so confusion. 放牛吃草, this word means just, let the cow eat the grass. But deeper meaning, whose metaphor is to give somebody enough freedom. There have a requires attention, "to give somebody enough freedom" maybe is praise or derogatory. The same situation, we need to see the sentence before and after to judgment this idiom that what it want to mean. Because everything if it not enough or too much that will have a problem.

Is “放牛吃草” a common Chinese idiom? I could not think of a situation when I would use this phrase. I suggest probably not to use it as it may cause awkwardness in conversations with a native Manderin speaker. Nevertheless, it means to give someone freedom in doing something. FYI.