A mud bath was a form of recreation in which the participants took a bath in a tub filled with mud.
In 2154, Commander Tucker and his engineering staff were working in a triple shift to create the mud bath the Tellarite ambassadors wanted. (ENT: "Babel One")
In 2368, Lwaxana Troi created a holoprogram of the Parallax colony and its mud baths. She enjoyed taking a bath in the mud and took Alexander Rozhenko and later Worf and her daughter Deanna with her. (TNG: "Cost Of Living")
Aboard Deep Space 9, Morn used to sleep in a mud bath in his own mud tub. (DS9: "Who Mourns for Morn?")
After stealing the warp core of the USS Voyager, Zet and Nar planned to visit the mud baths on the planet Eblar Prime. (VOY: "Renaissance Man")
In 2381, there were mud baths available on the Dove. Captain Carol Freeman tried the Tellarite mud bath. (LD: "Room for Growth")