What source of fuel is used by the body during long periods of low-intensity exercise, such as a day-long hike?

The fatty acids stored in the adipose tissues.

Explanation:

The adipose tissues are connective tissues that consist fat cells known as the adipocytes.

They are found all around the body. Those that are found under the skin are subcutaneous fat, while those that are found in the abdominal cavity, around the internal organs are visceral fats.

The adipose tissues store energy in form of fat, and insulate the body.