In a large bowl, beat the eggs, sugar, pumpkin, oil and vanilla. Combine the dry ingredients; add to the egg mixture and mix well. Stir in the nuts and proceed as the recipe instructs for baking.
This recipe will be tender and very moist when made with vegetable oil but will not achieve the height that it could have if made with shortening. When shortening is creamed, it incorporates bubbles into the fat that lead to increased height.
I do not suggest substituting oil for the shortening in the frosting. When made with oil, the frosting will lack body. If health concerns are an issue, vegetable oil has the same number of calories and fat grams as butter, even though it has less saturated fat. I would use butter over shortening for optimum flavor and texture. Your other option would be to combine the confectioners’ sugar and orange peel with just orange juice and use it as a glaze or drizzle.