Preheat oven to 350°F (175°C). Line a baking tray with parchment paper.
In a large bowl, rub together chilled butter, flour, and salt until the mixture resembles wet sand.
Pour in sweetened condensed milk. Mix gently with hands until a soft dough forms.
Scoop tablespoon-sized portions of dough. Roll into smooth balls.
Place dough balls on the baking tray, spacing slightly apart.
Bake for 12-15 minutes until bottoms are lightly golden (tops should stay pale).
Cool for 5 minutes, then roll warm cookies in powdered sugar.
Place cookies on a wire rack to cool completely.
Roll in powdered sugar again after cooling for a thick, snowy finish.