You're going to have to go through Chillbreath Caverns to find this gold key. Enter it through the entrance uphill from the Monorail System (no other entrance will work). Go towards the frozen lake once inside the cave, and head up the right slope. Continue along your path, skipping the bridge, and fighting everything you see. You will exit the cave eventually (should see some ruins), and the gold key will be right there in front of you.