Are you running a 5k mud run or a Toughmudder 12miler or etc? do some runs, upperbody strenght to help you pull yourself over obstacles, get your leg strenght going for you because you will need it. Dont go crazy overtraining, mudruns are meant for fun so its not a race unless you wanna treat it like one. I suggest a mix of bodyweight training and some weights, make it a full body workout just my opinion. Have fun!!
Some decent trail runs with solid vertical (anything around 1,000 feet or more for every 3 mi) will help build endurance, core strength and leg strength :-)
Im planning on one at the end of april as well. I already run the road and all the trails i can find so i think il b fine on that part. But l was told upper body strength is a must so iv been focusing alot more on that than usual.