I shake out my grooming bucket about every week.. I rinse my horse's pad every 3 days, and I try to clean my brushes out every time I use them with a metal curry or scrubbing them in the water bucket.. My hoof pick is always clean as I want his hooves to stay healthy and I think a dirty hoof pick wouldn't accomplish that.
But I don't really clean my saddle or bridle lately because I ran out of saddle soap.. I rinse off his bit though..
I USED to clean everything once a week, but I had a tack store nearby so I could grab what I needed without ordering online.