Thank heaven you're flying over grass!
Your goal is to get all the grit out of the engine with the least amount of work.
You can always completely disassemble, then clean thoroughly -- but that's often overkill.
Your goal is to clean the engine in a step by step process, always trying to keep any grit from getting into the engine.
It's best to do all of this before the mud dries -- if there's running water at the field and you'll have a chance to finish up as soon as you get home, that's a good time to start. Without turning the prop, rinse the outside of the engine to keep that mud from getting into things later.
When you're someplace quiet, and after the outside of the engine is clean, and without moving the prop, remove the venturi. Depending on the consistency of the mud involved, I usually like to remove the venturi before I dig the mud out of it -- that gets the mud as far away from the crankcase as possible, and it's the inside of the crankcase (and, hence, the engine's working parts) that we want to keep clean.
So, remove the venturi without moving the prop. Now look at the back of the venturi and at the crank. You're looking for two things: one, did any mud get all the way through the venturi (it often gets stopped by the spray bar if you have one), and two, was the crank valve open? If there's no trace of mud past the spray bar and if the crank valve was closed, then I breath a big sigh of relief. At this point, I'll usually wash the venturi thoroughly, reassemble, treat the engine to some after-run oil, and figure I'm good.
If there's mud past the spraybar, and especially if the crank valve is open, then you probably want to strip the engine down, clean each bit as thoroughly as you can, and reassemble. Use your judgment -- if the valve is open but there's no sign of mud, I'd probably reassemble and go fly.
Going forward, get a pair of nylon stockings from the store (be sure to ask so you get a pair in your size). Then rubber-band a scrap of nylon over your venturi, and that'll keep the mud out of the engine on future unscheduled landings.