Whether through musical notes, or morse code, or even in somehow using tempo in relation to the notes.
I have read Mozart was a notorious jokester for instance and I wonder if it extended into his music as well.
Likewise I have heard the Bach liked to compose with a BACH(G#) progression.
Or on a more modern note, during wars, if messages were encoded into the music played on army radio.
Many! The B-A-C-H progression is probably the most famous, having been referenced by Johann Sebastian himself, as well as Liszt, Schumann, and living composers like Arvo Part. http://www.wqxr.org/#!/story/277113-top-five-deployments-b-a-c-h/
A particular piece with a connection to cryptography is Edward Elgar's "Enigma" Variations, where each movement is named with a pseudonym for an acquaintance of the composer's, contains a variation of the theme which begins the piece, and Elgar cagily had said that there is a "dark saying" to which the theme is related. During his lifetime he never confirmed that anyone had guessed the connection, and he took the secret to his grave.
This is very difficult to answer. Mostly because it's hard to even portray the scope of musical borrowing in the history of music. In terms of secret messages, you could suppose that any instance of musical borrowing was done so as a secret of sorts. Whether it serves as the cantus firmus or some obscure sample in a rap song, musical borrowing has been as ubiquitous as music itself.
One of the famous examples of a "secret" message in music is Sir Edward Elgar's "Enigma Variations". The names of the movements are mostly abbreviations of people he knew. The movements are caricatures of those people. But at the same time, Elgar referenced that the theme itself was borrowed from source. This has been a point of contention among music scholars, with some ideas as to where it might have come from (note: this is just one of many ideas that have surfaced over the years).
For more on musical borrowing, there is an excellent entry in the Grove Musical Dictionary by Peter Burkholder. I also suggest checking out the Musical Borrowing bibliography (when it's back up) for more on various examples of musical borrowing.
One of the most stunning and explicit cases that I know of is the Lyric Suite, a work for string quartet written between 1925–26 by Alban Berg (a student of Schoenberg's). In 1977, composer and music theorist George Perle wrote about his discovery of a "secret program" for the work, the subject of three articles in The Musical Times ("The Secret Programme of the Lyric Suite, Parts I–3," Vol. 118 [August–October 1977, Nos. 1614–1616], available on JSTOR).
The Lyric Suite is a twelve-tone work, meaning that its musical language is based on an ordering of the twelve notes of the chromatic scale—a "row" of notes. Berg's row in this particular piece begins with F and ends with H (The German name for B-natural, the note right below C). In the manuscript—which had been hidden from public view for decades before Perle published his articles—Berg highlights these beginning and ending notes over and over again, connecting the literal dots; he also highlights whenever they're near two other notes, A and B (the German name for B-flat). It's one of several examples throughout the manuscript that the Lyric Suite is a dedication to Hanna Fuchs-Robetin, and is a gesture of (Alban) Berg's unrequited love for her.
This could have been written off as a coincidence were it not for a few other details in the manuscript (note that these annotations were certainly NOT in the published score). For one, the piece is dedicated "Für meine Hanna"; for another, in the preface, after Berg's colleague Erwin Stein writes in the preface about the constraints of twelve-tone composition, Berg has handwritten in the manuscript:
It has also, my Hanna, allowed me other freedoms! For example, that of secretly inserting our initials, H.F. and A.B., into this music, and of relating every movement and every section of every movement to our numbers, 10 and 23. I have written these, and much that has other meanings, into this score for you (for whom, and only for whom -- - in spite of the official dedication on the following page [to Berg's colleague, Alexander Zemlinsky] - - - every note of this work was written). May it be a small monument to a great love.' [Translation Perle's]
(Throughout the work, Berg plays with durations of 10 and 23 measures—numbers he associates with Hanna and himself, respectively.)
Alban Berg and Hanna Fuchs-Robetin were both married. Until 1977 Berg's personal legacy had been curated, in a way, by his wife Helene (Alban died of blood poisoning in 1935, and Helene outlived him by 41 years). Helene edited Berg's published letters, for example, which portray the couple in virtually nothing besides favorable light. Yet it's clear Alban was unsatisfied in his marriage. An excerpt from a letter to Hanna in 1931, also in Perle's article:
. . Not a day passes, not half a day, not a night, when I do not think of you, not a week, when I am not suddenly flooded by yearning, which submerges all my thoughts and feelings and wishes in an ardour which is not weaker by a breath than that of May 1925 - - only still shadowed by a grief which since that time rules me more and more, and which, for long time now, has made me into a double, or better said, a play-acting person.
I'd be happy to provide more details, but I'd suggest reading Perle's articles, if you can access them. They're not long (each one is five or six pages) and they're all exceptionally documented and detailed.
[Edited for formatting]
Haydn was famous for being a joker in his music; the Surprise symphony---maybe not as much of a joke, but the wit of the name 'surprise' is heard in the first few bars when the main subject is given as piano and then BAM you hear a massive C major chord!
Bach, on the other hand, is a different story. I know not of secret messages, however he did insert his name into music at certain points. Most infamous is the third voice of the final contrapunctus of the Art of Fugue, bwv 1080----- Bb, A, C, B natural----in German, Bb is called B; our B natural, to them, is called H. B, A, C, H. Odd that he never really used his name in earlier works; fitting perhaps that he died as he worked on this massive, thought-to-be four-voice fugue.
More on not-messages, but his abilities in counterpoint allowed him to insert many well-known subjects into his music---his cantatas, for example, call on ancient German chorales (basically hymns; think Luther, for example--the reformist). The subject of a chorale, when used in terms of polyphony around it, is called a cantus firmus. A ground subject which harmonies are built around. A famous example this is perhaps the chorale prelude Ich Ruf Zu Dir, Herr Jesu Christ BWV 639. The subject is given in the right hand, while altered to suit his thoughts. In many cantatas, some ariosos or arias or recitatives, you may hear an instrumental version of a chorale. (The tenor aria Meine Seele wartet from cantata 131, for example, the altos sing the firmus for Herr Jesus Christ, du Hochtest Gut).
The Musical Offering, BWV 1079, has a sectioned called the crab(?) canon. This subject (the King's subject, as it was called, given by Fredrick of Prussia, is the bass of the entire Offering) Bach devised in such a way it can be played backwards and forwards and sound musically divine. (link at the bottom). It is a part of the actual work 1079, though not called the crab canon, I don't think.
I don't know if I helped or anything but I hope the info was useful to some extent.
bach 1:21:15 for his name