Eamonn Murphy, 61, from Carrickfergus and 63-year-old John Murphy, who lived in Portrush, died on the mountains near Glencoe on Saturday.
A 46-year-old man from Scotland was also killed.
The Murphy family said Eamonn and John were very experienced climbers and had been walking in mountainous areas all their lives.
“They were not the sort of people to take unnecessary risks and were on an approved trail as part of an organized group when this accident happened,” they said.
“The emergency services have said that the group had done everything right and were wearing the correct clothing and carrying the right equipment for the conditions.”
The Murphy family thanked the group who tried to get the brothers out of the snow and also expressed sympathies to the family of the other man who died.
Relatives praised the efforts of the emergency teams who assisted in the rescue efforts, including the police, air force, navy and mountain rescue teams, and all the medical staff involved in the rescue.
They added in a statment: “Eamonn and John were both very experienced and lived for the outdoors. They were regular visitors to Scotland and this was a (Robert) Burns weekend trip which they did every year.
“They went out walking whenever they could both near and far. They walked close to home around Cave Hill in Belfast, the Mourne Mountains, in Italy and beyond and was something they enjoyed with a passion.
“We are obviously deeply upset by what has happened and now want to be left alone as a family to make the arrangements for the funerals and would request that the media respect our privacy at this time.”