Mix all ingredients together in a bowl until smooth.
Video
Notes
Let the sauce sit, covered, in the fridge for about an hour before serving it so the flavors have time to come together.
If the sauce is too thick, add a couple tablespoons of water or milk to thin it out until the desired consistency is reached.
Reduce the amount of Louisiana hot sauce and/or the horseradish for a less spicy sauce. Note, however, the flavor will not be as good.
If you want to make this taste even more homemade, you can certainly make the mayonnaise from scratch as well (homemade mayonnaise is just in a different league than the stuff at the store).