How can I clean mold off the back of a cowhide rug?

You should first start by flipping over the rug and using a wet/dry vacuum to suck out any remaining moisture from the back of the cowhide. Then you can create a solution by mixing a small amount of laundry detergent with water. Take a rag and dab/blot the solution into the mildew stain. Then, rinse the rug to remove the soap. Spray water onto the stain and use your wet/dry vacuum to fully suck out the water. Repeat this process a couple of times. You can then spritz the back of the rug with vinegar to disinfect the area. Let the vinegar disinfect the rug for about 5 minutes and suck up any remaining liquid with the vacuum once more.