If you live on a horse farm in a non arid climate, you will be dealing with mud at some point. It's inevitable. And frustrating. To tackle mud, you need to first know your enemy.
Often the local agricultural extension offices and soil conservation services will also have solutions that are pertinent to your area. Since implementing solutions for mud control are often time consuming and/or expensive, it is well worth doing as much research as possible for deciding how to tackle your mud issue.
Geotextiles are one form of mud control. Cow Carpet is specifically designed for livestock applications.
Other solutions are based on military technology that allowed heavy equipment to travel over uneven terrain. These have been made applicable to agricultural needs.
I used geotextile fabric for some of the muddy areas that I was dealing with and I have been pleased with the results. I would strongly suggest having the advice of someone familiar with mud management so you don't make mistakes that need to be corrected later.
As we are also interested in keeping as "green" as possible, it may be worth looking into recycled cement or recycled asphalt for some projects around the farm. They are relatively inexpensive compared to some of the other footing products. I have also found that 3/4 inch thick horse mats also work well in the very high traffic areas and are very easy to clean. Since I feed the hay under the overhangs, the mats keep the horses from accidently ingesting soil as well as keeping the area easier to clean.