A group of about 70 people - 10 of them adults - from the Cleveland Army Cadets Force were in the County Down mountains when the weather became treacherous.
An emergency operation was launched on Wednesday morning to assist the group, which included children aged 12 to 17.
The Northern Ireland Ambulance said 16 people had hypothermia.
Others had minor injuries.
In a statement on Facebook, the Cleveland Army Cadets Force said that "all cadets have now been recovered from the mountains and accounted for".
The alarm was raised at 11:13 BST on Wednesday. Coastguard, ambulance and helicopter crews were called to the scene.
Medical staff treated several of the children on the mountain.
The Northern Ireland Ambulance Service (NIAS) declared a major incident at 13:21 BST.
Ten accident and emergency crews, a hazardous area response team and Mountain Rescue went to the scene.