@EventHandler
private void onHorseJump(HorseJumpEvent event){
    Vector velocity = new Vector(0, 1000, 0);
    event.getEntity().setVelocity(velocity);
}

If this code is used on spigot 1.8.4, the horse will fly. The horse will even fly if jumped again in the air.

If it's used on 1.11.2, the horse will instantly lose all velocity and fall down.

I think there is a workaround with nms, but I haven't tried yet.