I have two whitetail deer hair on hides which i use as sleeping mats when out camping in the winter.
I dressed the hides , stretching them out on a frame, and worked them with a shoulder bone scraper until they lost some of their stiffness. They are air dried in the sun, and the hair is still firmly set in the hides. This same process is used by the Sami for their hair on hides. I also have a piece of bear hide , done in the same manner, and then smoked which I've used as a sitting pad when hunting for the last couple of years.
I agree with the suggestion of shaving the hide, and then rubbing off the stubble, as being your best option. Try a small section first and see if it works for you.