Put the flour, sugar and ground ginger in a mixing bowl or a food processor. Add the butter and rub in with your fingertips or process until the mixture resembles fine breadcrumbs.
Continue mixing, or squeeze the crumbs together with your hands to form a soft ball. Knead lightly, then roll out thinly between 2 pieces of nonstick baking paper.
Cut out snowmen shapes using a 10 cm (4 inch) biscuit cutter then transfer to ungreased baking sheets. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 7–8 minutes until pale golden. Leave to cool on the baking sheets then transfer to a wire rack.
Make the icing. Sift the icing sugar and ground ginger into a bowl. Gradually mix in the water to make a smooth thin icing. Spoon over the biscuits and allow to drizzle over the edges. Add the silver balls or tiny sweets for eyes, then leave to dry and harden.
Decorate the snowmen with scarves, hats and pompoms made from the ready-to-roll icing, sticking the pompoms with a little water. Pipe on small, black, smiling mouths. Leave to harden for 1 hour, before serving.