I think this was the final story in a collection of short stories, or possibly formed a coda to a longer single story.
A man is trying to cross a large ice range, based on stories of what might be on the other side. Others had tried and failed, died, or never returned. Many people believe there is nothing on the other side, or perhaps that the ice goes on forever. He sets off at a certain time of year - presumably the warmest/when the ice is at it's lowest. His journey is a gamble, as he doesn't know how far he will have to go or if there is even anything on the other side. The season begins to turn and the temperature drops, and he is cut off from retreating. Eventually he makes it over the ice range and there are indeed green lands and people on the other side.
The world it was set on may have been flat, or perhaps somehow ringed with ice - or it may simply have been that this land was cut off somehow.
The tech level was not advanced, though I do not believe it was a particularly fantastical setting. Low fantasy perhaps.
I read this a long time ago - perhaps 15-20 years, and I'm afraid I have no idea where.