To be no stranger to something means to be experienced in it, but the person is saying that they are new to these types of moods and are not experienced with them
Consider the statement "Great revelations of nature, of course, never fail to impress in one way or another, and I was not at all experienced in moods of the kind.". Is the statement "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." false? Yes/no/unknown