Hm, I don't think you should pickle horseradish, you make a paste of it.
First you shred the a big horseradish and then puree it fine. Add 1 teaspoon salt, 3 tablespoon lemon juice, white vinegar, 2 tablespoon heavy whipping cream. Mix together and put in an airtight glass container.
Pickles with horseradish are like this: you best buy Persian cucumbers,
2 ts salt, 1 ts horseradish, some fresh dill, 5 ts apple cider vinegar and water,
1 teasp black peppercorns and mustard seeds, 2 bay leaves, 3.5 oz. sugar
Scrub cucumbers very well and put in a bowl with water and salt and let it
sit for 24 hours. Prepare pickle glasses and add sliced cucumbers and horseradish.
Heat water in a skillet, add dill, bay leaves, sugar and other ingredients, boil it for 5 min and let it cool down and pour into glasses with cucumber and horseradish. Close glasses immediately and let it sit for 2 weeks in a dark, cool room or refrigerator.