A Nunchuk (or another Wii Remote) is used as the reins of the beast, and the Wii Remote in the pocket detects the player's movement on the seat, which can be used either for balance or, in one example, to indicate the gait of the horse: "gentle forward/backward motion = walking, fast forward/backward rocking motion = gallop."
While we don't feel any particular pull to play a game by bouncing on a cushion, we really want this controller idea to come to fruition -- because we know that every time we get to write about the Nintendo Bouncy Seat is going to be like Christmas morning. Seriously, Nintendo, thank you.