N.B. The screenshots and descriptions are for the iPhone/iPad version.

This is a history per horse of the activities undertaken via the 'Lists' option on the Home Screen. (Apart from riding, activities can include lunging, hand walking, horse walker etc.)
If you start a ride list for a particular day, allocate a horse to a rider or handler and enter any notes, the exercise history for that horse is automatically updated here.
This is therefore a 'read only' history which is populated by the activity you assign it in the 'List' for a particular day. If lists are used as a focal point for horse exercise, there is no reason to enter exercise separately for a particular horse.