The men made a call to emergency services at around 3pm on Thursday after they got into difficulties climbing a snow gully.
PSNI Search and Rescue were then transported to the scene from Belfast City Airport in the Irish military aircraft, which was in the region providing animal food relief to farmers.
The helicopter dropped the two rescue team members at the top of the gully which was heavy with snow and ice.
One crew member abseiled down to the climbers who were described as in a "very precarious position" on the mountain and winched them to safety.
They were given immediate care on board the helicopter.
A second team of three PSNI Search and Rescue members, who were training, were picked up at Newcastle and transported to the scene by an Irish Coastguard helicopter to provide additional help.
The men, who were uninjured, were brought to their car by the North West Mountain Rescue and were able to return home.
"This operation was resolved in two hours and was made possible through the close working relationship between the different rescue organisations," a police spokesperson said.
Police have warned the public to be aware of snow hazards not normally seen in Northern Ireland such as cornices and avalanche risks in areas affected by snow and strong winds.
"All walkers, even those with winter experience, should bear this in mind and consider the potential risks before embarking on any walks in these areas," the spokesperson added.