Combine sugar, butter, vinegar, boiling water and food coloring in a large heavy metal saucepan.
Cook over low heat until sugar dissolves. Increase heat to medium-high; boil without stirring about 10 minutes, until mixture reaches the hard-crack stage, or 290° to 310° on a candy thermometer. Remove from heat; stir in cinnamon candies and let stand until bubbles subside.
Insert sticks into apples. Dip apples into mixture; swirl to coat and dip into ice water to harden candy coating. Place on a lightly buttered baking pan until set. Store in a cool, dry place.