PA-28 Cherokee Pilot reported a loss of aircraft control during departure due to a down draft of air resulting in an off airport landing.

Narrative

Calculated W&B; checked weather and air density; put 10 gallons of fuel in each wing to keep the airplane light. I had myself and two passengers with me. We took off with an initial climb rate of 250-300 feet per minute. As we were getting ready to make our east turn and eventually head south we hit a downdraft of air to which we were unable to recover from without losing to much airspeed. Upon realization of the situation I immediately started proactively looking for safe places to land the airplane and reassess. I found what looked like an inactive private dirt road and made my landing safely with no incident. I contacted Tower and notified them of my decision. The authorities came out to verify we were all safe and that the situation was under control. I made the decision to unload both passengers and all luggage and had a friend drive them south to ZZZ that is 2;000 ft. lower in elevation. An official escorted me as I taxied the airplane safely through town to a road that was adequately suited for a proper takeoff. I departed without incident. I continued my flight south to ZZZ to pick up my passengers and continued home to ZZZ1 as planned without further incident.