Judith,
This is the best experience ever! I personally have seen Mickey, Minnie, Goofy, and many other characters on the carousel in Magic Kingdom behind Cinderella's Castle and Chip and Dale on the Dumbo ride also in Magic Kingdom, but it is very sporadic. I don't think there is any certain way of knowing when they appear, but I have noticed that they appear far more often during the
Extra Magic Hours in the evening almost before closing time and first thing in the mornings (also during the Extra Magic Hours) when there are not many people in the parks and you end up getting almost a private showing and the children more options of riding with the characters on a one to one basis many times. Keep your eyes open, and BELIEVE!
Try also communicating with the Cast Members, they have a wealth of information and sometimes they will throw you a bone (bring some dog biscuits in case you meet Pluto!)
Good Luck!!! I'll keep my fingers crossed for you!