Spiralize or grate the beets. If sprializing the beets it may be difficult to shape the latkes if the curls are too long. Place the spiralized beets in a bowl and snip through them in a few places with kitchen shears to make sure they are a shorter more manageable length. Sprinkle the beets evenly with the cumin, arrowroot and salt. Stir to combine well. Lightly beat the egg and stir it into the beets to combine well.
Heat ¼ inch of oil in a frying pan over medium-high heat. Once the oil is hot spoon circles of the beet mixture into the pan. They should be about three inches in diameter. Cook until the bottoms are golden brown and the latke is set, about two minutes. Flip and cook an additional two minutes, or until golden and crisp. Remove the latkes from the pan and repeat with the remaining beet mixure.
To serve top each latke with a ½ teaspoon of horseradish and a heaping tablespoon of the smoked fish. Serve warm.