For the dough, quickly knead the flour, sugar, egg and cold butter into a smooth dough. Form the dough into a ball, wrap in plastic and chill for about 30 minutes.
Roll out the dough on a floured work surface until about 1/2 cm thick. Use cookie cutters to cut out shapes (such as Santa Claus, deer, gift packages, snowmen, etc.). Line a baking sheet with parchment paper and place the cookies on the sheet. Bake for about 10 minutes at 200°C (approximately 400°F). Remove from the oven and let cool.
For the glaze, mix the powdered sugar and lemon juice into a thick glaze. Use food coloring to dye portions of the icing. Decorate the cookies with the icing, let dry and serve.