In theory, you don't need an ID to travel in the Schengen area as a citizen of the EU: https://europa.eu/youreurope/citizens/travel/entry-exit/eu-c...
Locals have been able to travel between the countries freely without a passport since 1954.
You'll need your ID to stay in a hotel/AirBnB though. So unless you squat or camp illegally, better have it with you.