Typically, hot chocolate mix packets will contain a minimal amount of caffeine. Cocoa powder does contain a small amount of caffeine, but it is significantly lower compared to coffee or tea. For example, the caffeine in hot cocoa is usually around 2-5 milligrams per cup where a cup of coffee can range from 95-165 milligrams of caffeine. If seeking caffeine in your cup of frozen hot chocolate, freeze coffee instead of chocolate milk in the ice cube tray.