It has been said that horse breeders do not admit to the existence of such a thing as a white horse; it is pale or grey, but not white, never white. Yet Binky is truly a white horse, a large, magnificent white horse, white not as snow but as milk, because milk has more life than snow. Binky has been for a long time now Death's current mount (time doesn't matter in the alternative reality in which Death resides).
Death had tried a skeletal horse, but that required him to stop often to wire the bits back on. He had also tried a fiery black horse, but that often stood in embarrassment with its bedding on fire. Death then acquired Binky, a flesh-and-blood real and biologically normal horse (no fire, etc). Like Death, Binky lives and works outside of time and does not age. He is very likely the most well-treated beast of burden in the whole of the Discworld.
Death regularly takes him to Jason Ogg – a son of Nanny Ogg and smith in the Ramtops – to get re-shod. Death himself appears in almost every novel of the Discworld chronicles; Binky can be assumed to be somewhere nearby, although he does not often get mentioned.
Binky has more significant appearances in Mort, Sourcery, Soul Music, and Thief of Time, on two of the four instances not only as horse of Death, but as one of the horses of the Four Horsemen of the Apocralypse.