As far as I know, they do have fur. But it's covered in moss.. Lichen, something.. That gives them their distinct color.
Quoted from the wiki;
'' Their moss-like skin color ranges from light green to blue and purple. However, the jungle trolls' bodies are covered in a short, soft fur which cause the trolls to appear purple or gray.[1] ''
Nice, clean explaination of Trolls. I like it a lot!