A horse has from immemorial time been a symbol of the spiritual as well as vital energies of the inner solar orb. Hence, when the next avatara is said to come riding a white horse, the meaning is that he comes infilled with the solar light or splendor -- an avatara or manifestation of a spiritual and intellectual solar energy which will carry all before it on earth.
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Brahmanical esotericism never taught that divinity descended into the animals as given in the legends. These names of different animals and men, like all zoological mythology, were chosen because of certain characteristic attributes. They actually represent ten degrees of advancing knowledge and growth in understanding -- ten degrees in the esoteric cycle -- as well as different evolutionary stages through which monads break through the lower spheres in order to express themselves on higher rungs of the evolutionary ladder of life. These names also represent the technical names given to neophytes in esoteric schools. The lowest chela was called a fish, the chela who had taken the second degree successfully was called a tortoise, and so forth, till the highest of all was called an incarnation of the sun -- a white horse in Hindu legend.
These avataric descents do not appertain solely to a race, root-race, globe, chain, or solar system, because nature repeats itself by analogy, and the same line of enlarging understanding of evolutionary development takes place in all the spheres mutatis mutandis. Thus these avataric descents can be ascribed to the solar system, the planetary chain as a whole, a globe, a root-race, and even to a subrace.