There isn't really any point in going to an off-road, or all-terrain tire, on a trailer. Traction isn't really an issue. A tire with tougher belts will help prevent damage from sharp rocks. Just going up a grade in load-range will get you a tougher tire carcass.
The best advice I can give regarding trailer tires when off the road, is to turn down your brake control. The brake control setting you use on the highway will cause the wheels to lockup when on low traction surfaces like dirt or gravel roads. And dragging a tire that is not rotating, across sharp rocks or even gravel, is a really excellent way to tear a tire. I personally have done exactly that.