Prepare the filling by mixing the chopped corned beef with the sauerkraut and cheese in a large bowl. Set aside.
Mix the softened cream cheese, Russian dressing, and prepared horseradish in a smaller bowl until well mixed.
Combine the cream cheese mixture and the corned beef mixture and mix well.
Mix the cornstarch with 2 tablespoons of water in a small bowl until dissolved.
Lay one egg roll wrapper on the counter in front of you with one of the points pointed toward you.
Add about 1/3 cup of filling to the egg roll in a line across the center of the egg roll wrapper, without any filling touching the sides.
Paint a bit of the cornstarch and water mixture with a finger or brush along the outside edge of the egg roll wrapper. This will help seal the egg rolls.
Roll the egg roll by folding the point of the wrapper closest to you up and over the middle of the filling. Then, tuck in each side. Finish rolling the egg roll. Roll it like you'd roll a burrito (see step-by-step images below for help.) Set the finished egg roll to the side.
Continue rolling the egg rolls until the filling is gone.
Heat oil in a deep-fat fryer or cast-iron skillet to about 350-F and fry the egg rolls, working in batches, for 3-4 minutes per side or until they're golden brown.
Drain on paper towels and serve immediately.