When building a cold room, location and access to good ventilation are important. Construct this room in the coolest part of the house, which traditionally is the basement, and install insulation to keep it insulated from the warmer air in the remainder of the house.
Ideal position is in a basement corner with two external walls. Insulate the ceiling and interior walls but leave the exterior walls uninsulated and unfinished. This allows the moisture from the soil to seep into the room, which in turn contributes to keeping the room cool. Ventilation should include both a warm air outlet and a cool air inlet. Use an insulating door and a vapor barrier on the internal walls.