Winterforce are great for softer dirt. I have seen them chunk up pretty badly on hardened dry dirt and clay.
For street tires that work well in rallycrosses, look for something with a blocky tread. I use 185/65, up a little from the stock size, but it will give some extra ground clearance, be a little cheaper and won't really hurt your performance or gearing too badly.
I have friends that use the PepBoys brand performance tires on their rallycross cars and always seem to finish well. I don't remember the name, but I remember them saying the tires were from PBoys, and that they were cheap(ish).
Rally tires are by far the best bet! I remember my first set, and I was able to drop a gear with the better traction. In other words, I used to use 2nd everywhere on street tires, but with rally tires, I could stretch 1st through most courses unless they were really long. It was a pretty amazing traction difference!