I find it fun (and good exercise) to wear boots and slog through sticky mud. The upsides are that shallow mud is easier-by-far to find, and it's frequently a challenge not to fall on your face in it, so if you do, and you get caught walking out with mud all over the front of you, saying "I fell" pretty much ends any question on why you're covered with mud. If you spend your time just walking around, without "falling", then the only thing that gets muddy are your boots, so cleanup is a snap!

Just bring a plastic bag to put the boots in, then wash them off when you get home.
It's only when you want to play in mud that's more than ankle deep that things get interesting. If you're somewhere cold, you'll want waders, such that you are never actually in danger of getting wet. (wet + cold = bad) Remember that waders, particularly the chest-height ones, can be a deathtrap to the unwary. I have an uncle that survived breaking through ice and having his chest waders fill, but only because he was a young man at the time, and there were 3 other uncles to help pull him out when it happened. Be careful to stay away from anyplace where mud + water depth exceed your navel. (even shallower stuff can be bad if you fall down)
Lukewarm weather is best for mudding. Too hot or cold and getting stuck becomes a really bad thing. I think cold weather is the most dangerous though, in that ice (especially down here in Arkansas) can be hidden by snow and can be strong enough to support your weight temporarily, then drop you into water, and most people going into the mud for fun want to do this where people aren't watching, so stuck and alone can mean stuck with no help.
The best advice would be to find someone you can depend on to go mudding with you, but while I type that I have to admit I've all-but never done that.
Hopefully, some of this rambling is worth reading. Good luck!
