I'm new at cake decorating, but here are my ideas. Pros out there might have better suggestions.
I would use royal icing with the grass tip (Wilton #233). You could also put a somewhat thick layer of icing (I think either buttercream or royal would work) and then texturize it with a small star tip. Use just the tip (no icing or bag) and push the tip into the icing then pull away. This also works on fondant.
i have done the 3d using the grass tip (233) on both of my elmo and cookie monster they turned out pretty furry look under my name if any quetions just pm me lots of luck i hope it helps