Sprinkler??..HA!..not here...
A sprinkler would turn my driveway into a nice skating rink tonight!--its 23 degrees here now!..our "mud" here is mostly clay..I bought my 74 K20 from an "Off Roader" who buried it quite a few times in the clay,judging by the amount of concrete looking clumps that were so firmly adhered to the undercarriage it took hammer blows to break it off!..
I had that truck since 1990--I washed the thing a hundred times,even used a pressure washer on it once!..I never succeeded in getting all the clay off the firewall where the tires had flung it!..stuff was like mortar,not mud!It was still there when it went in the crusher this July!....I sincerely doubt a sprinkler will remove much of the "mud" we have here..other states and places ,--maybe..depends of what type of dirt..
I'd say high pressure,and HOT water with soap is best..even the car washes here,which had decent pressure and hot soapy water,didn't seem to phase the mud on my truck though..a Steam Cleaning might have done the trick..either that or sandblasting..

..
I read somewhere in an off roading book if you apply liberal amounts of Linseed oil to the frame and underbody,it will keep mud from adhereing so well..supposedly keeps rust at bay too,and lasts quite awile before you need to apply it again..many guys around here use drain oil on their trucks frames and undersides..it works,I've seen several "oldies" that are still in great shape,despite daily use in salty winter weather..
I think Deisel engines used oil is best--the soot makes it cling better to the frame,and doesn't wash off easily..one local garage made a habit of disposing of the used oil on his customers cars by spraying the underneath of their cars with it!..all the grandmothers with their 30+ year old Impala's and Buicks had mint undercarriages in their cars that went there for service..

..