I have found that it depends on the time of year for me. There are times of the year where I have a problem with mud. I put some sand on my walkways but the runs just get so wet. I inspect their feet and the deciding factor is:
do the feet stay caked or do they get cleaned off later in the day by walking on some other area of the pen?
If they stay caked then I DO clean their feet. And try to remedy the situation like open another pen for grass to walk on to clean their feet. I have movable fencing so I can open an emergency temporary pen attached to the main run. It is very flimsy fencing is why I don't like to use it.
Feet???
I have four feather footed breeds, and I've not yet had to bathe their feet. But we don't have a big mud issue around here, and I don't show chickens. If any of them ended up with clumped mud on their feathers, I'd wash their feet though. Perhaps you should consider sand if you have a muddy run???