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Line 12 muffin cups with paper liners.
When ready to bake, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 350 degrees F and preheat, lid closed, for 10 to 15 minutes.
In a large bowl, beat the eggs, vanilla, and orange zest until foamy with an electric mixer. Stir in the oil. Gradually beat in the sugar until the mixture is thick. Add the flour, cinnamon, baking soda and salt and beat until mixed.
Stir in the carrots and walnuts, if using. Spoon the batter into the prepared muffin cups, filling each about two-thirds full.
Place a doubled piece of heavy-duty foil on the grill grate and put the muffin tin on top of the foil. Bake the cupcakes for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
Transfer the tin of cupcakes to a wire rack to cool completely.
Make the icing: Beat the butter with the cream cheese in a bowl until well-blended. Beat in the vanilla, then gradually add the confectioners' sugar, beating on low speed. The mixture will be slightly stiff.
Add 1 tablespoon of milk and beat on high speed, adding milk a teaspoon at a time as needed to achieve an icing with a spreadable consistency.
Ice the cooled cupcakes using a table knife, small spatula, or a decorating tip.