Preheat oven to 375 degrees F. In large bowl, with mixer at low speed, beat sugar and butter until blended.
Increase speed to high; beat until light and fluffy, about 5 minutes. At medium speed, beat in ricotta, pumpkin puree, cinnamon, vanilla, and eggs until well combined.
Reduce speed to low. Add flour, baking powder, and salt; beat until dough forms.
Drop dough by level tablespoons, about 2 inches apart, onto ungreased large cookie sheet.
Bake about 20 minutes or until cookies are very lightly golden (cookies will be soft). Remove cookies to wire rack to cool. Repeat with remaining dough.
When cookies are cool, prepare icing: In small bowl, stir confectioners' sugar and milk until smooth. With small metal spatula or knife, spread icing on cookies; sprinkle with sugar crystals. Set cookies aside to allow icing to dry completely.