Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with aluminum foil.

Arrange bread pieces on the baking sheet.

Toast in the preheated oven for 5 minutes. Transfer to a plate and keep oven on.

Combine mayonnaise, ketchup, onion, and horseradish in a small bowl. Stir until evenly combined.

Place 12 dill pickle slices on the foil-lined baking sheet. Evenly distribute corned beef over the pickle slices. Top each with a teaspoon of mayo mixture. Place a piece of toasted bread over the top of the mayo mixture. Top each with a piece of cheese.

Bake in the preheated oven for 5 minutes. Remove from oven and top each slider with remaining pickle slices. Stick a toothpick in each slider to serve.