A change of socks refreshes your feet, and you want to be able to wash the perspiration out once each day at least. For cross-country going or mountain climbing, high socks with trouser bottoms tucked in make walking smoother.
For bicycling, the rules about foot gear are just the opposite. Here you need, soft supple shoes instead of a wide firm base. The bike tires take the punishment, and your feet, in supplying power, must be flexible and free. Here sneakers are permissible, if they have ridged soles, though they will slip on the pedals when they are wet. Well-fitted soft-soled moccasins are good, and even the famous barefoot sandal with steel arch support is comfortable for biking. In warm wet weather, biking barefoot solves a lot of problems. Your choice of socks depends mostly on the weather. Light-weight wool is the favorite of cyclists too. And the new brushed nylon or orlon are even better. Take along some tasty beef jerky for a snack.