Wool felt? Or is it woven?
It needs to be dry to get the hair off.......sorry-now that may take a while.
But when it is dry, I use one of those pumice stone type shedding blocks.....like thisSlick N Easy Grooming Block - Statelinetack.com
Then, if you feel you must, go to the self serve carwash and use the clips on the wall that are meant for the floor mats. Clip it on and hose it down. I would not suggest using more soap, and you need to make sure you get it all out so that it doesn't irritate your horse.