Cabin Base: Fill a piping bag with frosting. Pipe a line of frosting along one side of a churro; lay frosting-side down on a serving platter. Repeat with 3 additional churros to form a square. Repeat with a second layer of churros, stacking them frosting side down on top of base layer. Repeat until walls are 4 churros high. Stick toothpicks vertically through churros at each corner for structural stability.
Roof: Center a graham cracker across the top of the cabin, using frosting to adhere it to the tops of the cabin walls. Lay a second graham cracker next to it; it will overhang the side of the cabin a bit. Adhere it with frosting. Repeat with a third graham cracker on the other side. Measure and cut 2 pieces of red licorice to the same length as the graham crackers, about 4x 3/4 inches; glue with frosting down the center of the middle graham cracker about 3 inches apart. These will hold up the A-frame roof. To form the A-frame, frost the long sides of 2 graham crackers and lean them together so top long sides meet and bottom long sides are set just inside the licorice lines. Decorate roof with licorice and gumdrops as desired.
Cabin Door: Break a graham cracker in half widthwise, spread a thin layer of frosting on one side, then decorate with candy canes and holiday sprinkles. Frost backside of door and stick it to the front of the log cabin.
Windows: Break a graham cracker into quarters. Spread 3 quarters with a thin layer of frosting and decorate as desired. Frost backside of windows and stick them to sides and back of cabin.
Icicles and Snow: Pipe frosting icicles along roofline, sprinkle coconut around cabin, and sift confectioners' sugar over the top.