I had mud & drainage problems too. I had all the top soil removed from the paddocks/dry lots, (luckily I have sandy soil underneath), & have grading done so any water flows into a hay field & had a french drain installed.
Pastures are not used if they are wet & every other year I have them aerated to avoid standing water. That made a huge difference as the horses really pack the soil, more than I ever realized.
Just some ideas.