Beat butter and cream cheese together in a bowl using an electric mixer until smooth and creamy. Sift flour and salt together into a bowl; stir into creamed butter until dough holds together. Cover bowl with plastic wrap and chill, 3 hours to overnight.
Press 1 walnut into each date and press closed.
Preheat oven to 375 degrees F (190 degrees C).
Spread a pastry cloth over a work surface and sprinkle generously with confectioners' sugar. Roll chilled dough into 1/8-inch thick rectangle on the prepared work surface. Cut dough into 3 1/2 x 1 1/2-inch strips using a pastry wheel or pizza cutter.
Place 1 stuffed date in the center of each strip. Roll strip around date and sprinkle with confectioners' sugar. Arrange cookies, folded side-down, on a baking sheet.
Bake in the preheated oven until lightly browned, 15 to 18 minutes.