To trudge is to:

To trudge means to walk heavily or with effort. This term conveys the idea of moving with a sense of fatigue or labor, often due to difficult conditions such as deep snow or being very tired. The physicality associated with trudging implies that the person is putting a significant amount of energy into their movement, which typically suggests a slow and heavy gait.

In contrast, the other options describe different forms of movement that are generally more lighthearted or quick. Sprinting, skipping, or dancing all connote a sense of ease, speed, or joy, which does not align with the overtones of exhaustion and effort conveyed by trudging. Therefore, the definition of trudging focuses on the struggle and heavy nature of the walking style, reinforcing that "walk heavily or with effort" is the correct understanding of the term.