The Bug
When riding a horse with slow falling, both you and the horse will still take damage upon landing, even if both of you have the slow falling potion effect. Note that the horse still falls slowly regardless of if the player is riding it or not, it just doesn't prevent the damage.
Steps to Reproduce
Summon a horse and give it the slow falling effect.
/summon minecraft:horse ~ ~ ~ {Tame:1b,SaddleItem:{id:"minecraft:saddle",Count:1b}} /effect give @e[type=minecraft:horse,limit=1,sort=nearest] minecraft:slow_falling 999 0
Relog, to avoid MC-121788
Switch into survival mode, mount the horse, and ride it off a high cliff.
Wait for the horse to slowly fall to the ground. It still takes damage.
This is NOT A DUPLICATE of MC-121788. That issue is entirely separate.
MC-121788 Is a bug in which effects don't apply until relog
MC-152258 Is a bug in which effects DO apply but regardless of relog, slow falling does not prevent fall damage on a ridden horse