Using absorbent bedding is great, but in an outdoor exposed environment it's just going to get soggy and bogged down. Like others have said, chunky material like wood chips will let the water drain through and they hold up well. But even so, the real key is to be able to keep that surface material separated from the wet ground below... and if you've ever seen chickens be chickens, you know they scratch the bedding down to the dirt looking for bugs.... which can mix everything together and create a still bigger muddy mess when rain comes along.
I think I have a pretty good system for keeping the mud at bay. We get a lot of rain here in Oregon! My coop has 2 small covered attached runs which open up to a larger exposed run area (it's actually the narrow fenced side yard of my house). It's been muddy there in the past, and in searching for a solution I "borrowed" this
mud management idea from Newland Poultry in the UK.
What makes this system work so well is that the ground (mud) and the surface material (wood chips) are kept separate by a sturdy barrier. I first cleared the area, laid PVC poultry netting and attached it to the ground using garden pins, then put my wood chips on top. The chips never get mixed with the muddy ground below! It's amazing! My chickens still enjoy scratching and finding bugs and the PVC material is easy on their feet and drains well.
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These pictures were taken before I built my new coop in this area.
When we were having a large tree on our property cut down last year, I had the tree-cutter guys leave me all the contents from the wood chipper. It's all spread very thick and I do rake them occasionally to level the potholes. My girls seem happy and healthy and not muddy at all!
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Chickens are very susceptible to mud-born pathogens and a wet environment is a breeding ground for coccidiosis. I can't do anything about the rain and I can't dry out the wood chips, but at least there's no mud. I've added some logs and perches at different heights throughout this little yard to offer escape from the wet ground because they just don't seem to want to stay under cover where it's dry, unless it's pouring down rain.
I use regular pine shavings in the covered run areas and sand underneath the coop. But I have to say that those covered areas probably wouldn't stay dry if I didn't have a gutter for my roof to redirect the rain runoff somewhere else.
now everyone has their own coop, but this was when I had first gotten all of my chickens and ducks. They were babies, and it stayed an absolute MESS. But I realized over time it just got worse, using puppy pads under your bedding helps tremendously, and it also makes changing the bedding easier. Just roll up the pads and toss into a garbage bag. I also found putting a giant outdoor garbage can with a good heavy duty lawn and garden bag helps with easy disposal and it doesn’t rip like the other bags! I sit mine beside the coop when I’m cleaning it out. At first I was tossing the used bedding into the woods but as they get bigger, they get NASTIER
My thought is to do deep bedding, which is essentially in-coop composting and requires clean-out only once or twice a year as I understand it, so if I go that route the “chicken pad” idea won’t work for me...however it’s all up in the air at this point (I’m getting tiny bantams, and only a few, so I am also thinking of keeping them indoors and cleaning out every day or two...kind of the polar opposite of deep bedding...) SO—every idea is welcome! Thank you for sharing your thoughts and experience with me 
