Heat oven to 350°F. Line 24 mini muffins cups with paper or foil candy cups (about 1 1/4 inch). Pat maraschino cherries dry with paper towel. Flatten each cookie slightly. Place 1 cherry in middle of each flattened cookie. Shape dough around cherry to completely cover; shape dough-wrapped cherry into ball. Place dough balls into candy cups.
Bake 20 to 25 minutes or until golden brown. Cool 10 minutes; remove candy cups from pans. Cool completely, about 20 minutes.
In small bowl, mix powdered sugar, melted butter, almond extract and enough milk for spreading consistency. Spread over cookies; sprinkle with red sugar.