Preheat oven to 350 degrees. Line a standard muffin tin with paper liners.
In a medium bowl, whisk together flours, baking soda, salt, and finely chopped hazelnuts. In another medium bowl, whisk together oil, buttermilk, eggs, granulated sugar, vanilla, orange zest, and carrots until combined. Fold oil mixture into flour mixture until just combined. Divide batter evenly among lined cups, filling each three-quarters full.
Bake cupcakes until golden and a toothpick inserted in centers comes out clean, about 23 minutes. Let cupcakes cool in pan 15 minutes, then transfer to a wire rack and let cool completely.
In a small bowl, stir together cream cheese and confectioners' sugar until smooth; season with a pinch of salt. Frost cupcakes, then sprinkle with coarsely chopped hazelnuts.