Minutes later, they were stuck in the midst of a blizzard.
"There was crazy wind and no visibility when we came off the lift," he said yesterday.
"We rode off the track. We thought we knew where it was, but we must have ridden over it without noticing it and continued until we found tracks which we then followed way off the run.
"We called emergency services early then set to making a snow cave type shelter against a big pine on a little ridge. We expected the visibility to improve the following day so we were pretty sure we would be found eventually, but we were expecting to spend the night there."
Mr Neilson, from Pleasant Point in South Canterbury, contacted a friend to keep topping up his cellphone with credit, and he stayed on the line with emergency services for "hours".
Authorities were able to establish roughly where the three were by using the signal from the cellphone. But it still took hours for rescuers to find the exact spot.
"It [the cellphone] basically saved our lives," Mr Neilson said.
"It was a bit depressing to discover they didn't know where we were ... I was on the phone for hours. They used shotguns and flares, with us relaying back what we could see and where."
An infrared camera was also used in the search.
He said being rescued did not "feel like a sure thing" at times, so he was relieved when the search party arrived to walk them off the ridge.
When help finally arrived, it was in the form of about 100 Greek Army and special forces searchers.
"It was an amazing effort by the Greeks, we were really pleased with how they handled it. They were really glad to find us, we were getting a bit sick of the cold, I must say."
Mr Dunne wrote on Facebook afterwards: "Coldest I've ever been, proper Bear Grylls s*** ... mad."
The three spent a night in hospital suffering from the effects of being in the cold for so long. But none had serious injuries and they were soon discharged.
"I'm struggling with temperature regulation a bit, but we're all fine," said Mr Neilson.
"I don't think Tana or Jamie enjoyed the experience. But I've done dumber things. Still, I would have liked to spend the night in the hotel instead - it was pretty bloody cold."
Mr Neilson also told friends about his ordeal on Facebook.
"Just spent a night lost in a blizzard in the Greek mountains huddled up in a snow cave thing ... Spent the morning in hospital ... Awesome. Still a wicked weekend never to be forgotten. Special thanks to ... anyone else who helped keep us alive this weekend, it is very much appreciated - you're all legends," he wrote.
"Was fun building a shelter. Was a good challenge. Pity we couldn't get a few photos, but shouldn't forget it in a hurry. Nice and warm again now."
Mr Dunne, from Auckland, has been travelling the world for about four years, visiting Cambodia, Thailand, Morocco, France, Italy, Bangladesh, Nepal and India before taking a job with Sailing Holidays, a Greece-based company offering tours around the Greek Islands.
