A primer on how to interpret the meaning of animals in your dreams 
[See bottom for a link to a BIG list of animals and what they can symbolize in dreams]
Language is full of sayings such as “proud as a lion,” “slippery as a fish,” and “free as a bird”—rich with symbolism for dreams to use. Dreams bring to life these sayings, and they use animals to tell stories full of personal meaning and significance.
For example, a person dreamed about fish dying in a fishbowl filled with bad water, symbolically warning of an oncoming bladder infection. The fishbowl symbolizes the dreamer’s bladder, and fish live in water, so the dying fish indicate something wrong with the liquid in her bladder. The dream even recommended a solution: shown as chunks of cucumber in the water. Cucumber makes water more alkaline. The dreamer took the advice and nipped the infection in the bud.
In a dream about finding a white horse in a snowstorm, the horse symbolizes ability to move forward under treacherous personal conditions. Horses are strong and this dreamer needed her inner strength at that time of her life more than ever.
In a dream about three kittens drowned in a pool but one still alive, kitten-like qualities in the dreamer are symbolically “killed off,” but one kitten left alive shows that the dreamer is trying to preserve a part of himself from extinction: the gently playful side of himself succumbing to teenage peer pressure to toughen up.
I’m RadOwl.
Other associations can be made with fish, horses, and kittens though. For instance, if your only personal experience with a horse is when one kicked you, you aren’t as likely to dream about a horse in a good context. What an animal in your dream means to you matters more than pat definitions like the kind found in typical dream dictionaries!
Animal symbolism in dreams is personal
Consider the characteristics and qualities of animals that appear in your dreams. A dog to one person is a loyal companion; to another person it’s a noisy nuisance. Both are common perceptions—which one fits your dream?
To find out what an animal in your dream means, associate the animal with your experiences, perceptions, and feelings. Also consider figures of speech that might apply, and caricatures from books, movies, cartoons and TV shows that imbue everything from ants to birds to elephants with human qualities and voices. Your experience with, and impressions of, the creatures that appear in your dreams help determine what they symbolize.
Usually, common associations with animals and creatures in dreams is the basis of the symbolism. Dogs are friendly and loyal. Horses are strong and fast. But dreams can use your personal experiences, too, and it next to impossible for an outsider to guess what it means. For example, in a dream about a raccoon attack, the symbolism is based on a childhood experience with raccoons.
This dream about raccoon attack is based on a personal experience, not common associations with raccoons.
Dreams use animals to create comparisons with people and behavior
Generally, the wilder the creature, the more instinctive or primitive your related emotions, behaviors, or instincts. We all have instincts reminiscent of certain animals or creatures. For example, rabbits and bulls are notorious for the instinct to mate. Gazelles and deer are known for the instinct to run. Lions and dogs are known for the instinct to protect territory. People have those instincts and display those behaviors, too. Dreams readily pick up on those associations and connections and use them to create symbolism.
Also, people are compared to animals and creatures in figures of speech like “stealthy as a cat,” “friendly as a dog,” and “treacherous as a snake.” One image can sum up a person’s behavior or personality. Comparisons to animals can be highly accurate ways of describing what we observe in people—and in ourselves.
Animals can be used to symbolize the dynamics of a situation. For example, a school of fish swimming together can symbolize a group of likeminded people. An elephant can symbolize something that’s inevitable, that can’t be stopped. The common interpretation is that elephants are wise and are association with strong memory, but you really have to understand the symbolism of an elephant within the context of the dream-story.
Animal symbols understood in context of the dream
Dream interpretation, you say? Hmm, I wonder if any great books can help you with that….
As with all symbolism, the meaning is interpreted by tieing together details and analyzing the symbol within the context of the story. Just because an elephant is in a dream doesn’t mean it represents something that can’t be stopped. But if the elephant pushes forward through barricades, it’s a supporting detail that suggests the symbolism is related to something that can’t be stopped.
Pay attention to the age of the animal. A puppy, cub, or other young animal can represent something new or young in the dreamer. An old dog might be a play on the phrase “you old dog.” It could symbolize an elder figure or something coming to an end.
Parents of young children are known to dream about baby animals, because comparisons between young children and young animals are easy to make—and in fact are made frequently in media and everyday conversation. For example, a mother might call her child “my little tiger,” then dream about a baby tiger and not realize the relationship between it and her child.
And keep in mind, animals can be used as props in a story. In other words, the white rabbit you chase down a hole might relate to something rabbit-like about you, like the desire to hide or protect yourself. Or it might be a prop in a story about finding out how deep the rabbit hole really goes.