Using a sharp knife, cut apple in half vertically. Using the thinnest setting on a mandoline, cut 24 slices from apple. Discard seeds.
In the work bowl of a food processor, process together cheese, mayonnaise, horseradish, salt, and pepper until well combined.
Spread 1 tablespoon cheese mixture onto each frozen bread slice. Arrange a layer of arugula on cheese side of 3 bread slices. Stagger 8 apple slices on top of arugula. Shingle approximately 2 turkey slices on top of apples. Top each with a remaining bread slice, cheese side down, to make 3 sandwiches.
Using a serrated knife in a gently sawing motion, trim crusts from sandwiches. Cut each sandwich diagonally into 4 triangles. Serve immediately, or cover with damp paper towels, place in an airtight container, and refrigerate until ready to serve.
Recipe by TeaTime Magazine at https://teatimemagazine.com/smoked-turkey-red-apple-tea-sandwiches/