I don't see fur used this way as coming close trapping the amount of air that down and synthetic insulation does. Plus you will have the large weight penalty of the leather the fur is attached to. There will also be the bulk issue. I truly think you're attempting to hang from the wrong tree with this one.
While there is room for many improvements and different styles in hammocking, I don't believe that everything needs to be reinvented considering the materials available today.