Beat butter and sugar at medium speed with an electric mixer until creamy. Add flour, almonds, and extract, beating at low speed until well blended. Stir in cherries.
Shape dough into 1-inch balls. Place on ungreased baking sheets.
Bake at 325° for 18 to 22 minutes or until lightly browned. Remove to wire racks; cool 2 minutes. Roll cookies in powdered sugar; cool completely on wire racks.