Sift together flour, soda, salt, and spices; add to creamed mixture, beating well. Cover and refrigerate at least 1 hour.
Divide dough in half. Working with one portion at a time, place dough on a heavily floured surface; roll to 1/4-inch thickness. Cut dough with a floured doughnut cutter.
Heat 3 to 4 inches of oil to 375°; drop in 3 or 4 doughnuts at a time. Cook 1 minute or until golden brown on one side; turn and cook other side. Drain on paper towels; sprinkle with powdered sugar. Repeat cutting and frying procedures with remaining dough.