In medium bowl, combine cooked rice and vinegar; mix well. Cover; refrigerate 30 minutes or until cold.
In small bowl, combine cream cheese and horseradish; mix well. Place each tortilla on 12-inch square of plastic wrap. Spread about 2 tablespoons cream cheese mixture over each tortilla, spreading to edges. Arrange corned beef slices over cream cheese, overlapping slices and leaving 1 inch of top and bottom edges of each tortilla uncovered.
Spoon about 1/3 cup cold rice mixture across center of each tortilla; press firmly into strip about 2 inches wide and 1/2 inch thick.
Quarter cucumber lengthwise. Reserve 3 sections for another use. Remove seeds from cucumber quarter; cut into 3 thin lengthwise strips. Press 1 strip into center of each rice strip. Cut roasted peppers into thin strips. Place next to cucumber to form long red stripe.
On each tortilla, mound another 1/3 cup rice mixture over cucumber and roasted pepper. With wet hands, form rice into firm rolls, completely covering cucumber and roasted pepper.
Beginning at bottom edge, roll each tortilla firmly around rice. Wrap each roll securely in plastic wrap. Refrigerate at least 4 hours or until well chilled. To serve, trim uneven ends; cut each roll into eight 3/4-inch-thick slices.