Wading through mud is a difficult and unpleasant task that requires a lot of effort. The term 'WADE through mud' can be broken down into two words, 'WADE' and 'SLOG'. To 'WADE' means to walk through water or mud with some difficulty, while 'SLOG' means to move slowly and laboriously. Both words describe the same action, but 'SLOG' implies more effort and difficulty. Therefore, the crossword solutions for the term 'WADE through mud' are 'SLOSH' and 'SLOG'.