Cut ten strips of freezer paper into 8x3-inch rectangles. Arrange them shiny-side-down on two baking sheets. Set aside.
Use a mixer on medium-high speed to combine meringue powder, sugar, peppermint extract, and water until mixture forms stiff peaks and loses its sheen, about 5 minutes.
Divide meringue into small bowls and tint with food coloring as desired. Transfer each color to a zip-top bag and snip off a corner. Pipe X's, O's, and dots onto each strip. Let the candy dry completely, about 4 hours.