(1) If you are being chased in a dream, what is chasing you probably symbolizes something you are afraid of, either in your external life or - more commonly - in your inner self, your unconscious. For example, a woman who dreams of being chased by men is probably afraid of sex. (Freud would add that her dreams present, in disguise, an unconscious, repressed desire for sex.)
(2) If you are doing the chasing, the ‘you’ in your dream is probably your conscious ego and the thing you are chasing is almost certainly some part of yourself that frightens you. Chasing it away means disowning it, banishing it from your conscious life. It might be much better to try to integrate it into your conscious life. At the very least, get to know it and understand it.... A Dictionary of Dream Symbols
Red cows appearing in a dream are a positive, hopeful omen of peace and plenty. In Persia, these represented the spirit of dawn, which is filled with renewed vitality and courage.
In Greece, an all-white cow was ail alternative symbol for the moon.
A natural source of nourishment (see Meat).
Among the Celts and people of Scandinavian heritages, an emblem of continued provision.
A sacred animal in India, representative of life itself.
The milk from cows is used to nourish kings and priests, so this dream may represent self-nourishment.
Among ancient Egyptians, Indians, and Scandinavians, the cow was an emblem of the Great iMother, and some psychological schools still ascribe this image as possibly being linked to your own mother (see Women).... The Language of Dreams