If the soil has too much nitrogen, it will not grow roots well (it doesn't really need thick roots in that case). Horseradish, while delicious, is basically a weed, and does best when treated as such. You want to basically keep it nitrogen-starved. Best soil for horseradish is nitrogen-poor, which causes much better root growth. (Also make sure the soil is loose). Pick the worst piece of dirt you have. Cultivate to about 2 feet deep. Mix in sand, perlite, or coconut coir if necessary, to keep the soil loose. The only nutrients you should add are phosphorus and sulfur (I use epsom salts in water for the sulfur). Only water as necessary. You need to make it struggle a bit for it to put its energy into the roots. I doubt you get frost where you are, but cold weather (and frost) helps the roots develop better flavor. Good luck!

- Mark