The Exiled Lands or the entrance Conan used to access it is either in or near Stygia.

The snow in the Exiled Lands is artificial. The Witch Queen actually makes this so clear in her description of seeing the Exiled Lands for the first time, that it kind of feels like a forced insert by the writers specifically to prove the tundra is artificial: “In the north were mountains, but not the snow-covered mountains that we had seen on our journey, just jagged rocky peaks.”