In video, this is sometimes an example of white hats versus black hats - in early westerns, especially black and white, the filmmakers would put white hats on the good cowboys and black hats on the evil ones as a quick visual distinguisher that appears tacky today.
But white or white-looking grey horses are special in fantasy fiction. Gandalf rides Shadowfax. The Companions in Mercedes Lackey's Valdemar are white. Over and over again, western authors put the special hero, the king, etc on a white horse.
Plain and simple, white horses have a mythological significance all over the world. The Celtic mother goddess is sometimes portrayed as a white mare. Pegasus is also white and Odin's eight-legged steed Sleipnir is generally considered to be grey.
White horses have been sacrificed and used in divination ceremonies. At some Hindu weddings the groom arrives riding a white horse and accompanied by the youngest male member of his family (No matter how young). In this case, the white horse symbolizes the hoped-for fertility of the match.
So, the plain truth of it is that white horses are a trope because they have always been a trope - and there's nothing wrong with using it. Just be aware that it is a trope (and therefore ripe to be subverted).
A true white Thoroughbred, courtesy of Kersti Nebelsiek.