Good question, not that i am aware of BUT i also wouldn't think continued exposure to only mud would be good, if they can get away from it for breaks of time, i think it would be fine.
The areas around my pools are muddy, but my main flock free ranges so have plenty of areas not muddy, plus are in housing at night. Even the calls have created quite the muddy mess but do have areas of grass and they too have housing.
I gather your feeling you are excessively muddy? are they penned?
I usually put grass cuttings down n it's soaks up the mud and looks good for a few days i I rake it up when it turns and smells but today we have had a lot of rain and a friend of mine said watch for mud rot this is from a horse owner , it's never muddy for too long thanks to the neighbours and the grass lol
I see, there are other ideas too, horses are totally different and that is rain rot, there is hoof rot too, sheep can suffer from that as well. Ducks love mud but you want them to get a break from it, i think that is the key and an ability to rinse so access to good bathing is of importance.
Perhaps in the pools and pond thread there is info for better drainage and mud reduction.
I learned last year that you really want to be careful adding organic material (straw, grass, leaves, etc) over mud. It decomposes and turns to yuck city. I have found the best thing here is the Barn Lime, safe for use around animals, not hydrated for really bad spots. Then sand and pea gravel to improve drainage. But pea gravel does need a base, otherwise it will get walked on and pressed down into the mud and disappear.
I most of the areas where it stays wet I put down landscaping material then river rock over top of that, the river rock is round so easier on the feet, and the landscaping material keep them from pushing the rock down into the mud. I have also used the barn lime and DE to keep smell at minimum but the LS material and rock works best.