Mix the cream cheese with the horseradish and finely chopped chives. Stir this well and season with salt and pepper if necessary.
Spread 4 of the six slices of bread with the cream cheese mixture. Top two slices of bread with the salmon and the other two with the spinach leaves.
On top of the salmon, place the cucumber ribbons and then the sandwich with the spinach goes on top again. Cover with the last sandwich and cut in half if necessary. Serve immediately.