My wife and I - we're both in our late 60s - loved hiking two times in the Parc Natural: once up to the Betlem Ermitage from the Betlem side, and once from the main parking lot about 7 km from Arta, where we were staying at the first-rate Hotel Forn Nou.
We were both ready to experience some nature after two weeks in cities (Paris and Barcelona) and were not disappointed. There are many routes to choose from as a previous reviewer has anicely described. At the parking lot, there are good descriptions of the trail networks describing their level of difficultly and time required.
In early November, the weather was warm, perfect hiking conditions and only a few other hikers and cyclists crossing paths. Wear decent walking shoes - you don't necessarily need hiking boots, hiking poles are good for inclines - and bring water and snacks for the longer treks. This is a wonderful natural resource, well maintained, with an intriguing balance of human culture and natural beauty. One of Arta's - and Mallorca's - hidden treasures.