Combine water, rice and cinnamon in a large bowl. Cover; let sit overnight.
Pour rice mixture (including cinnamon sticks) into blender; cover. Blend on high for 3 to 4 minutes or until mixture is as smooth as possible. Strain mixture through an extra fine sieve into a medium saucepan, pressing the rice solids until only a dry paste remains; discard paste.
Add sweetened condensed milk and milk to saucepan. Cook over medium heat, stirring frequently, for 5 minutes or until horchata is warm. Pour into cups; serve sprinkled with ground cinnamon, if desired.