The horse should be Horse-type
Its super effective against grass (horses eat grass), rock (horses walk on asphalt), dark (horses ride at night. See: Paul Revere)
Horse-type moves are resisted by Ice (Their poor hoovies get cold), Electric (Internet has dealt with enough horse), and Ghost (difficult to ride a horse if dead)
It’s weak to fire (horses probably can’t be on fire for long), water (can’t change horses mid stream-based attack), and electric (ONLY zeus’s horses are good around lighting stuff and if we make them we give it lightning rod obv)
It resists Grass (self explanatory), Dragon (self explanatory), Fighting (You can smack your horse a bunch in Ocarina of Time), and Fairy (horse in Cinderella was unphased being created by a fairy godmother)