Walking

This is your default mode of transportation. Unlike previous games, your transportation doesn't affect Food consumption or anything. The only difference between Walking and riding Horses is that you can't outrun monsters on foot.
Compare Walking to other Vehicles
Horse

Related

Foot

Actions/Food 2
Traverses Grass, Woods
Blocked By Water, Mountains

Foot

Food/14 Actions 7
Traverses Grass, Woods
Blocked By Water, Mountains

Walking

Food per Tile 0.19
Notes Normal movement, cannot cross mountains or water
Walking is your normal form of transportation. You can walk on most terrain, even damaging terrain like swamps, and you'll use less Food than you will on a Horse. If you want to open up new horizons and save on Food costs, though, find a Frigate or a Plane.