Are you talking about thick western saddle pads? I have the best luck using a pressure nozzle on my water hose at the barn and then letting them dry out in the sun/wind.
I suppose some people do but I never use soap on mine because I'm paranoid about not getting it all rinsed out and then having it irritate a horse's back. Of course, that's providing that all the horses I use it on are healthy with no skin issues. If one comes up with girth itch or something, I'll wash it thoroughly with an anti-everything (fungal, bacterial, microbial, etc) soap several times and then use about 10 times as much water as I need to make sure I've got all the soap out.
I've just been using a regular trigger spray nozzle to clean mine for years though I keep meaning to get one of those powerjet nozzles
that they advertise on TV.