If you attempt an overrun while mounted, your mount makes the Strength check to determine the success or failure of the overrun attack (and applies its size modifier, rather than yours). If you have the Trample feat and attempt an overrun while mounted, your target may not choose to avoid you, and if you knock your opponent prone with the overrun, your mount may make one hoof attack against your opponent.
But what if the player has a mount that is not a horse? Say a bison which lacks a hoof attack?
Would you use the bison's gore attack as opposed to a hoof? Since I am assuming the rules were written with only horse mounts in mind and the hoof is the horse's primary attack?
Is this just something up to DM discretion?