Preheat oven to 350. Grease or line 12 cupcake wells.
Make cupcakes: In large bowl, cream together butter and sugar. Add eggs, beat well. Add the baking powder, cinnamon and salt. Stir. Add the flour alternately with the apple cider until thoroughly combined. Pour into prepared cupcake pan, filling each cup 3/4 way full. Bake 20 minutes or until a toothpick inserted in the center of the center cupcake comes out clean. Cool completely.
Make Frosting: Put the apple cider in a small pan and bring to a boil over high heat. Continue to boil until the cider is reduced to about 2 tablespoons (it will be slightly syrupy). Set aside to cool completely. With an electric mixer, beat together cooled reduced cider, cream cheese, pinch of salt, and 1 cup of the powdered sugar. Add enough additional powdered sugar for desired frosting texture.