There is a horse in the movie, it's just shown out of focus or in extreme close up. This is one of Louise's memories of her daughter, when she exits the ship after deciding to take off her suit to interact with the aliens in person: she remembers her daughter interacting with a horse in a stable. Says the film's editor Joe Walker:
Many things were just grabbed moments that were sort of very emotive and beautiful, a hand touching a baby’s hand in a cart, or an out-of-focus shot of a horse in a stable. They could have gone anywhere. Trying to build that into the narrative and marble this narrative through with these little glimpses of a memory, if you like.
Says the film's director Denis Villeneuve:
For me, the scene that expresses most the movie, is the way the little girl is seeing the world, when she sees nature. The one shot that is very important to me, there is a shot where she sees a horse. That is one of the most important shots of the movie.
The usage of out of focus shots and extreme close-ups is prevalent in these scenes and conveys the personal yet amorphous nature of memories. You can see the horse (and also hear its hooves and see a silhouette of a hand holding its reins) right before the 50 minute mark. Here are images of the horse in the background and its muzzle up close: