How you make your mashed potatoes is completely dependent on how you like them. Adjust your buttermilk depending on how thick you like them and the horseradish depending on how spicy you want them.
To cook the potatoes, add to a large pot, cover completely with water, cover, and bring to a boil over high heat. Once the water is boiling, reduce heat to low and simmer until extremely tender, about 20 minutes.
Drain completely. Add potatoes to the bowl of a stand mixer with the paddle attachment. Add butter, buttermilk, and horseradish and blend until you reach your desired consistency. Add more of any ingredient, as well as a fair amount of salt and pepper, until desired result is achieved.
Serve immediately or refrigerate and heat up before serving if making ahead.