However, Morgan Freeman was not in "Whatever Happened to Baby Jane." The film was released in 1962, and Morgan Freeman's acting career began in the 1970s.
The ice cream scene in "Whatever Happened to Baby Jane?" features Victor Buono, who plays the character of Edwin Flagg, the kind and caring neighbor who takes care of Blanche Hudson (played by Bette Davis) after her sister Jane (played by Joan Crawford) incapacitates her.
It's possible that the memorable scene, with its dark humor and the chilling contrast between the ice cream's sweetness and the underlying tension, might have stuck in your mind and led you to think of Morgan Freeman's voice, which often lends itself to delivering both warmth and gravitas.