What Edmund rides in the film is not a Unicorn at all, just a "plain" Talking Horse. In the brothers' training scene, the first sight of Peter's Unicorn lets us know, even without the Unicorn saying anything, that Peter has been given a fabulous creature to ride on. But we don't find out that Edmund also has a more-than-ordinary horse UNTIL the horse talks to him. Which reminds me: although I understand that "Philip," the name given to that horse in the movie, was the name of the man who did his voice, this name is appropriate in its own right--because it is rooted in "hippos," the Greek word that MEANS "horse."
As for the objection by "Susan Pevinsie," Mr. Lewis does say that Talking Horses are not used for riding _except_ in emergencies, when "everyone must contribute." The battle against Jadis, WITH the preceding training, counts as a time for Talking Horses to make a contribution.
Joseph Ravitts, author of "Southward the Tigers" (Writing Club)