Exit the room the only way you can, but be ready to fight two Crystal Porcupines in the tunnel ahead. They will roll at you from different directions and generally make your life miserable. The good news is that, if you die, you won't have to fight the knight or the Frozen Covetous Demon again.
Walk up the tunnel they came from, and when you come to a fork in the road, hug the left wall and open the door there for a shortcut back to the Lower Garrison bonfire. Beware of the Frozen Porcupine waiting when you open the door.
Head back to the fork in the tunnel and go right to a clearing where there are five Frozen Porcupines and four Frozen Golems, three of whom will reanimate if you kill an enemy near them. Use ranged weapons to kill or coax the Frozen Porcupines toward your position and retreat into the cave if necessary to create separation. Use the same strategy for any reanimated Frozen Golems.
Once defeated, pillage two corpses in the area for Charcoal Pine Resin x 5 and Pharros' Lockstone x 1. Enter the door, take the elevator up, and you'll find yourself on the opposite side of the bridge that you couldn't cross earlier after the courtyard.