The term 'trudge through mud' can be described by three crossword solutions: PLOD, SLOSH, and SLOG. PLOD is a verb meaning to walk slowly and heavily, often with great effort. SLOSH is a verb meaning to move clumsily or noisily in a liquid or soft substance. SLOG is a verb meaning to work hard and steadily, especially at a dull or monotonous task. All three words describe the action of trudging through mud, which is a difficult and tiring task that requires a lot of effort.