Physiology of skin and leather: why do salt borders occur?
The two processes are quite different: On leather shoes no active transport takes place. The salt either comes with the snow (most likely most of it) when the streets get salted to avoid ice. Your shoe soaks up the salt-water mixture and when the water dries up, the salt stays behind. The other possibility (more for new leather shoes) is that water goes into the leather and dissolves salts, which remain from the tanning process of the leather. With older shoes I have never observed this "snow marks" in the summer when the shoes got wet in rain.
Using a wet cloth removes the salt, subsequent treatment of the shoe prevents that water can enter the leather.

The skin is quite different: Here we have living cells and an active transport of water through pores when you body get warm. This is to cool you and prevent overheating and since the body fluids contain salt, so does sweat.