I've seen Eeyore in Town Square and Cruella in Toontown in November, that was definitely odd.
Pinocchio and Geppetto were there too, but that happens pretty often.
Random characters... I was waiting to meet Snow White when she was out at the wishing well when Mary Poppins and Bert walked past, with Peppermint the Penguin trailing behind them. As you can imagine the Snow White line got one person shorter very quickly.

We ended up following them all over Fantasyland, but I got my Penguin picture.
I've also seen Brer Bear and Brer Fox in Critter Country, they're not always there. Does that count as random? They're all over the place there too, I've seen them near the Pooh Meet and Greet, hiding in the Splash Mountain queue and on the bridge.
Sometimes characters show up on the path near BTM, but that seems to be on hold while Santa is there.
There's also been at least one character at the entrance near the Mickey floral during our November stay. Usually it were Aladdin and Jasmine, but sometimes other princesses, Cruella or the Evil Queen. Apparently we missed the White Rabbit there by ten minutes.
In DCA there's normally one or two characters near the Animation Academy, but it's been a while since I've seen a more rare character there. Usually it's Sulley, Max or Stitch or Playhouse Disney characters.