Bring water to a boil in a large saucepan; stir in milk, rice, sugar, and salt. Reduce heat to low; cover and cook 1 hour (do not allow to boil), stirring twice. Remove from heat; allow to cool to room temperature. Cover and refrigerate overnight.
Beat whipping cream in a large mixing bowl until soft peaks form. Fold in pineapple, cherries, vanilla, and cold rice mixture. Spoon into individual serving bowls, and serve chilled.