Roy:
In my readings of Hollywood history back in the 'thirties and 'forties, during the "Golden Age" of movie production, I've never come across any indication that the Moguls had their own private railroad cars. Though many of the major studios (MGM, Warners, Fox) had their financial offices in New York City near Wall Street, the actual day to day running of the studios was done in Hollywood.
I would think that when Studio excecs like Mayer of MGM, Jack Warner, Darryl Zanuck of Fox or Adolf Zukor of Paramount were called back to New York for conferences, they probably used suites on the various luxury trains (the Santa Fe "Chief" seemed to be the most popular) for their journey's back East.
Hollywood was known for occasionally hiring special trains for cast and crew members if a movie location took the production out of the area of Los Angeles. One rather famous one was the Southern Pacific train hired by Fox films to transport the crew and cast of John Ford's THE IRON HORSE from Hollywood to Nevada in 1925, where the entire train became 'home' to the company for location filming in the Nevada desert for some time. The same thing happened later in 1939, when a special section of Union Pacific's "Los Angeles Limited" transported second unit crews and actors to Utah for location filming on deMille's UNION PACIFIC. However, at this time, the train was used only for transportation to and from the location.
But as far as private railroad cars bought specifically for studio execs, I've never come across any information that this was ever the case.
Tom