Maybe wearable, integrated dehumidification is a bit too much of an ask to start with, and not easy to implement without customization. But perhaps there's an easier way to get stuff done:

By drying the boots more effectively while the guys are resting. The question then becomes: is running 5015-style radial blowers enough to get them somewhat dry?

Personnel sleeping in a trench. Two pairs of boots are soaked and standing around - probably not getting dry throughout the night. (source)