Here is a quick video Walkthrough of the Snow Ruins, showing the paths both to the Shortcut Stairway and the Isolated Stairway on each floor. Freyr's actions in moving as quickly as possible through each chamber, irrespective of damage to himself or his Silver Wolf are not recommended. In particular, it is better to destroy the arched wires connected to each explosive device, whether Eye Generator or Cannon, rather than attacking the device directly. This is NOT a combat tutorial. It is intended simply to show the paths that you need to take to reach each set of stairs.
This video was requested by Sue. I hope it is useful!