To be no stranger to something means to be experienced in it, so the person is saying that they are not new to these types of moods and are in fact experienced with them.
Context: "Great revelations of nature, of course, never fail to impress in one way or another, and I was thoroughly experienced in moods of the kind." Claim: "Great revelations of nature, of course, never fail to impress in one way or another, and I was no stranger to moods of the kind."
Considering the context, is the claim true, false, or unknown?