In large bowl of an electric mixer, beat shortening and granulated sugar until creamy; beat in molasses and water. In another bowl, stir together flour, salt, baking soda, ginger, nutmeg, and allspice; gradually add to shortening mixture, blending thoroughly. Cover tightly with plastic wrap and refrigerate until firm (about 2 hours).
Meanwhile, prepare foundation for cabin by covering a 12-inch square of stiff cardboard with foil. Also prepare patterns for cutting logs: cut lightweight cardboard into a 4 by 6-inch rectangle (for the roof); ½-inch-wide strips that are 2, 3-1/2 and 6 inches long (for logs); and a ½-inch square (for spacers).
With a floured rolling pin, roll out a third of the dough on a floured board to a thickness of 1/8 inch (keep remaining dough refrigerated). Make 2 roof sections by cutting around roof pattern with a sharp knife; transfer carefully to a lightly greased baking sheet.
Roll out scraps and all remaining dough to a thickness of 3/8 inch. Then cut out eight 2-inch-long longs, two 3-1/2-inch-long logs, seventeen 6-inch-long logs, and 30 spacers (1/2-inch squares). Transfer cookies to lightly greased baking sheets (bake separately from roof sections), arranging about 1 inch apart. From remaining dough, cut out trees or other decorative details. Extra spacers can be used for chimney and stepping stones.
Bake in a 350 degree oven for 12 to 15 minutes or until just firm to the touch (cookies will harden as they cool). As soon as roof section is baked, lay pattern on each section and evenly trim one long edge (where the 2 sections will meet). Let cookies cool briefly on baking sheets, then transfer to racks and let cool completely. If not assembling cabin at once, package airtight; freeze if desired.
Prepare icing. With a pastry brush, paint foil-covered foundation with icing, then sift some of the powdered sugar over icing to cover lightly. Assembly cabin, following steps 1 through 4 above and using icing as glue wherever logs join. Decorate as desired with extra shapes.
In most dry climates, cabin will keep for about 1 week. In humid areas, cookies may absorb moisture and start to sag, so plan to keep cabin for only 2 or 3 days before eating.