A fur effect essentially means adding texture to a flat surface. There are plenty of minis of animals that use non-textured surfaces to depict areas where fur or hair would be short (horses, for example). Adding texture to these surfaces can make a mini quite a bit more dynamic. For example:
To attain this effect, I used a sort of basic base-shade-highlight approach, only all of the areas of shading/highlighting were invented as I went.
I started out with a medium brown (P3 Idrian Flesh which I tinted slightly toward purple in order to make the brown seem brighter). Then drew short lines of fur onto him with a thin brush in a much darker brown color (something like P3 Umbral Umber or Battlefield Brown). This is your shading layer, so while you are adding in these dark lines, make sure to also put this color into the areas you'e like shaded on the finished mini.
When drawing these lines, follow the musculature of the mini. Super Dungeon minis don't have as detailed musculature as some other lines, but here you can see that the lines follow the muscles on his arms. More over, there are places on the mini that suggest tufts of fur (on his arms and beard, for example).
After that, it is time to highlight up. This is done using the same short line method, but now you should be using a lighter color. For this mini, I used the base color, then did several layers adding in more and more of a yellow-white to the mix (combined with the purple, this helps the brown seem brighter).
As you add more layers, treat this like most highlighting. Cover a smaller area with each pass, and highlight towards raised areas. The biggest difference here is that rather than blending the layers together, you are simply adding short lines as you go. The last pass, I actually just went around the face and hit the highest raised areas.
That's about it. As I use this technique more, I'll come back and update this write up with new insights.