Cleaning Shoes With Fake Fur on Them

You might try burying the fur part of the boots in a box holding a layer of cornstarch or fine cornmeal, and "combing" it through the fur repeatedly. It should absorb much of the oils that have adhered to the fur. Take the box with the boots and cornstarch outside to shake free and comb the fur free of the starch to check if it has helped. If it leaves the fur too powdery looking, simply vacuum it. Repeat as needed.