To make the cupcakes, preheat the oven to 350°F. Line 12 muffin cups with paper liners.
In a medium bowl, whisk the flour, baking powder, cinnamon and salt to blend; set aside. In a large bowl, whisk the granulated sugar, eggs and vanilla to blend. Slowly add the oil, whisking to blend well. Using a wooden spoon, stir in the flour mixture. Using a rubber spatula, fold in carrots, raisins and walnuts.
Divide the batter among the prepared muffin cups, using about ¼ cup batter for each cupcake. Bake for about 20 minutes, or until a toothpick inserted in the center of a cupcake comes out with just a few moist crumbs attached. Transfer the pan to a cooling rack and cool for 10 minutes, then transfer the cupcakes to the rack and cool completely.
To make the frosting, add ingredients to the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl, using a handheld mixer). Beat about 6 minutes, or until smooth, fluffy, and creamy.
Spread the frosting over the tops of the cupcakes.
Make-ahead: The frosted cupcakes will keep for up to 2 days, stored airtight in the refrigerator. Serve the cupcakes cold or at room temperature.
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