Instead of what is specifically labeled pea gravel and thus more expensive, order 1/4-10 (quarter-ten) gravel. It is small, but it is not as smooth, less expensive, and does not have that "walking on marbles" effect.
While large gravel is obviously not good, regular driveway gravel should be fine with an unshod horse. We used 3/4 minus, and the horses thought I had given them a back scratcher.
Geo-textile is best for keeping your gravel from disappearing into the mire, but I used garden weed block in a small area and it worked. Old, free carpeting is a redneck solution that also works.
While they are grading, have them create swales to redirect any surface water. Be careful not to create a bowl —ask me how I know...
Horses for Clean Water is an excellent website that addresses various approaches to improving drainage. Alayne Bickle also writes articles for Horse.com, so they have many useful articles on the subject.