Quarter cucumber lengthwise, cutting off and discarding rounded ends. Stir together cream cheese, chives, horseradish, salt, and pepper to taste until combined well. Pat cucumber dry. Arrange enough salmon to completely wrap 1 cucumber quarter in 1 layer on a sheet of plastic wrap, then spread with a thin layer of cream cheese mixture. Wrap coated salmon around cucumber quarter to cover completely, pressing gently to help it adhere. Repeat with remaining cucumber quarters. (You may have leftover salmon.) Cut rolls crosswise into 3/4-inch pieces.