Combine first 3 ingredients in a saucepan, stirring well.
Place cinnamon sticks and remaining 3 ingredients on a 6-inch square of cheesecloth; tie with string. Add spice bag to cider mixture.
Bring to a simmer over medium-high heat, stirring occasionally. Reduce heat to low, and cook, uncovered, 15 minutes, stirring occasionally. Discard spice bag. Pour into individual mugs, and serve warm.