As a World War one reenactor -

You deal with it as best you can.

A large part of being a soldier in this, or any other period, but particularly the period before rubber soles, is taking care of your feet. In the period leading up to the Great War, there were a number of foot remedies available ( Whale oil was used) but with the onset of Trench Warfare and cases of Trench Foot, regular foot inspection became the norm and footpowder and regular removal of socks and boots became the norm, as well as loose binding of the puttees. This article speaks to this topic, however it is uncited, but was supposedly sourced from the THE WESTERN JOURNAL OF MEDICINE, in the June 1990 edition.

Despite this, my experiance in the far less dangerous Trenches here in the states is similar, and I will outline the care we take to prevent foot injury:

1. Boots are "dubbed in" meaning a waterproofing preperation is applied to prevent water from penetrating the leather, which has a secondary effect of protecting your feet.

2. We wear puttees that close the top of the boot against debris, but are not waterproof. We avoid wading into water, but sometimes you'll slide into a puddle at the bottom of a shellhope that is particularly nasty ( dead horse for instance ) and you don't want that in your boots.

3. Regular removal of boots and socks, and changing socks to a dry pair after the Corporal inspects the feet and you apply powder. Dry socks are important, and warming the feet by the fire and applying powder keeps the platoon running, hence why our corporal was in charge of this. The Literature indicates company officers had this task, but in our case, our Sergent put the Corporals to this task and they did it well.