Unless its crusted with grime, sweat and hair, you dont want to wash your felt pad to offen. A good rub with a curry brush to loosen the hair, and a damp sponge (no soap) for any dirt spots. If this is done after every ride, it will stay in good shape. If its crusty and filthy, you can hose it off, starting from the middle of the pad and work your way out. Hand to dry on a fence rail (do not lay flat, it will trap the water and dirt... let is all drain away from the center of the pad.
I try to avoid ever washing my felt pads, they last so much longer.
I sometimes put a weee thin felt pad under my good pads to keep them clean. They have less than 1/4" thick pads that can simply be tossed out at the end of the season, because they are cheap. Keeps your expensive pad looking (and smelling) new!