I was reading this thread and read of a couple folks with horses dealing with mud. I live outside Eureka CA, a few miles from the coast, and constant rain is a problems here as well. Incredibly, I solved the mud problem.
I have a 40x40 paddock attached to a 30x48 barn. In the paddock area, I laid down geotextile paper, which is the stuff they lay under roads, and comes in 12' wide rolls. I got it at our local United Rental yard. Pull it good and tight. What I did is got several dumptruck loads of 5/8 crushed rock and put it over the top of it. It was recommended to me to use crushed granite, but we can't get that around here. The thing you want is crusher dust. For a while, you will have to bring in additional loads of rock to fill in, but after a few months, a layer of fine sand / rock will start to build up under the 5/8 rock and form a hard surface, kind of like road base does. We've had this surface down now for around 3 years, and it is a nice hard surface that gives under the horse's hoofs somewhat. This area used to be a foot to foot and a half of mud just from people and tractors on it, now, horses can walk on it without sinking in even an inch.
There are two keys. One is the geotextile cloth, which keeps the mud separate from the rock, and the crushed dust, which develops into that hard surface. I didn't think about it at the time, but this process might be helped by putting a thin layer of road base under the crushed rock when starting off. The second is constant scooping of the poop. We scoop at least three times a day, you do not want the poop getting mixed into the rock in large quantities, or you will just create a mud pit on top of the cloth.
This might be a pricey solution, but the results are astounding, it really works. During heavy rains, this area actually has a stream running across it, and it's hard as a rock, no mud!
I have pictures of the construction on my Facebook page, which I would be happy to share upon request. I don't have any recent photos, but if anyone would like some, I'd be happy to take some and share them.
Stan