Drain all your fluids, tranny and diffs as well. If you have the ability drop the oil pan and clean it out. The mud won't drain out thru the drain hole. Change all the fluids and then see what its like. No need to run to a mechanic just yet.
Check the coolant but it should be ok, probably won't need to change that but both diffs and the engine and tranny and t-case will all need to drained. After the covers are off the diffs use a can of brake clean to rinse them out, probably a full can per diff.
If its an auto, BEFORE YOU DRIVE IT ANYMORE, get the pan off and clean it and change the filter. For a manual tranny(and t-case) drain, refill, drive for a week or so then repeat.
If you cann't change your own fluids you may as well learn now of you will find 4 wheeling to be a VERY expensive hobby.