In a bowl, combine rice and 10 cups water; cover and chill until grains break easily when squeezed, about 24 hours, or up to 2 days.
In a blender, whirl about 2 cups of the rice mixture with sugar, vanilla, and cinnamon until sugar is dissolved and mixture is smooth; pour into a large bowl or pitcher (at least 3 1/2 qt.). Whirl remaining rice mixture without seasonings, in batches if necessary; add to bowl and stir until well blended with flavored batch. Taste, and add more sugar if desired.
Just before serving, stir mixture (ground rice will have settled to bottom). Fill glasses with ice cubes, then horchata.