In a large bowl, cream together the butter and sugar until smooth. Beat in the eggs, one at a time, mixing well after each.
Combine flour, baking powder, and salt; stir into the sugar mixture. Cover dough and chill for at least one hour.
Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets. On a floured surface, roll the dough out to 1/2 inch thick and cut into desired shapes using cookie cutters.
Place 2 inches apart on to the prepared baking sheets.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely. To make frosting, mix together the confectioners' sugar, oil and 1 teaspoon vanilla until smooth. gradually add enough hot water to achieve a spreadable consistency.
