What leisure activity involves walking and climbing through the steep sides of a river and its valley?

C is the appropriate choice as it specifically refers to an activity where participants walk through the steep sides of a river and its valley, often involving navigating rocky terrain and water channels. Gorge walking allows individuals to experience the natural beauty of river valleys while also engaging in physical exertion and adventure.

River rafting involves navigating a river's current in an inflatable raft, typically on larger bodies of water with rapids, rather than the steep sides and narrow paths of a valley. Canyoning is similar but focuses more on the descent through canyons, often incorporating techniques such as jumping, swimming, and rappelling, which may not prominently feature walking along the steep sides. Hiking generally refers to walking over trails in nature, not necessarily focused on river valleys and steep sides specifically. Hence, gorge walking is the most precise answer for the activity described.