Medical teams have arrived at the scene and are treating the group, who are understood to be army cadets on a camping trip.
An Army spokesman added: "We can confirm that all Army cadets caught in today's inclement weather on the Mourne Mountains are safe and accounted for".
Last year, the Mourne Mountains were voted Britain's best view in a survey.
Coastguard, paramedics and helicopter crews are now on the scene in the Mourne Mountains in Northern Ireland.
The Coastguard said on Wednesday afternoon that most of the group were being walked down the mountain to safety but up to 20 people may require stretcher evacuation as they are suffering from exposure.
In a statement, the United Kingdom coastguard said up to 70 people were involved in the incident.
A number of people are said to have sustained lower leg injuries.More news: Apple sales boosted by apps and music
The Northern Ireland Ambulance said 16 of the group are suffering from hypothermia and some had suffered minor injuries.
"We must admit that a huge support operation swung into help, we are very grateful to the police, search and rescue, and the ambulance service". The emergency team set up a base at Annalong community hall to treat the injured.
"There have been a handful of ankle injuries and some are suffering a little bit from the cold", he added.
Coastguard, ambulance and helicopter crews have been dispatched to the scene after a number of people became stranded.
The rescue operation involved 63 youngsters from the Middlesbrough area, aged between 12 and 17, along with their adult leaders.
'Please God all will be ok'.
According to the report, mountain rescue teams pull 46 people off the site but 17 are yet to be evacuated after helicopters were grounded. "Drivers should seek an alternative route".