Very true they appear frequently in books for children; not only Harry Potter but also Narnia,the Golden Compass, Pan's Labyrinth, LOTR ... and the list goes on.

For those that are a mixture of animals, try looking at Ted Andrew's books on Animal Speak. Ted has a lot of wisdom in understanding what animals can teach us through their symbolic meaning. As for those that are part animal, part human, once you find the animal meaning, ask yourself 'what does that mean to a human?' For example, a horse is symbolic of freedom. What would freedom mean, or look like to a man/woman? I find this approach more helpful than an esoteric, mystery school approach as the latter can be quite subjective does not necessarily offer any useful advice.
Hope this has been of help.