Wash cucumbers, slice into 1/4-inch thick rounds, and place in a heated, sterilized mason jar with horseradish and fresh dill weed.
Set a large pot over medium heat and add vinegar, sugar, water, garlic and pickling spices. Bring the brine to a boil then pour over cucumbers and horseradish in still-hot mason jar and seal lid. Allow to cool to room temperature before refrigerating. You can serve once chilled, but for best flavor serve after the pickles have been left overnight.