When the oil is hot, grab a handful of rings from the buttermilk and let the excess drip off. Toss them in the cornmeal, coating all surfaces. Shake off any excess before dropping them in the oil. Fry for about a minute and a half, until golden and crispy. Drain on paper towels. (Fry the onions in batches to avoid crowding the pan.)
Mix the horseradish aioli ingredients together and serve with the onion strings.