In a medium bowl combine cheese, green onion, and horseradish. Cover and chill until ready to use.
Preheat oven to 375 degrees F. Unfold one of the pastry sheets on a lightly floured surface. With the tines of a fork, generously prick the pastry. Use a 2-inch round cutter to cut pastry into circles. Transfer circles to an ungreased baking sheet. Brush pastry lightly with milk. Sprinkle with salt. Bake for 10 to 12 minutes or until golden brown. Cool on a wire rack. Repeat with remaining pastry sheet.
To assemble, use a knife to split the baked pastries horizontally. Spread about 1 teaspoon of the cheese mixture on the cut side of each bottom pastry. Top with several cucumber slices and radish slices. Spread the cut side of each top pastry with about 1 teaspoon of the cheese mixture. Place on top of radish slices.