Joseph F. Smith says that the White Horse Prophecy is a "ridiculous story" and is not an authentic prophecy of Joseph Smith's.
Joseph F. Smith, Conference Report (Salt Lake City: The Church of Jesus Christ of Latter-day Saints, 1918): 57-58
The ridiculous story about the “red horse,” and “the black horse,” and “the white horse,” and a lot of trash that has been circulated about and printed and sent around as a great revelation given by the Prophet Joseph Smith, is a matter that was gotten up, I understand, some ten years after the death of the Prophet Joseph Smith, by two of our brethren who put together some broken sentences from the Prophet that they may have heard from time to time, and formulated this so-called revelation out of it, and it was never spoken by the prophet in the manner in which they have put it forth. It is simply false; that is all there is to it.