Scots Sergeant Duncan Slater, 34, who served in the RAF infantry regiment, is aiming to become the first double amputee to complete the gruelling 173-mile after setting out on the Virgin Money South Pole Allied Challenge with Team Glenfiddich on Sunday.
The group, which also includes Prince Harry, have now covered more than 14 miles amid biting winds and temperatures that have dropped as low as -35ºC.
The team is now leading rival groups Team Noom Coach and Team Soldier On.
Team Glenfiddich is mostly drawn from wounded servicemen and women from the UK as is competing against other injured service personnel from the United States and the Commonwealth.
Victoria Nicholson, Expedition Manager, said that some of Team Soldier On have not acclimatised as well as the other teams.
The second day was said to be tough for all team members, who are dragging 80-90kg sleds full of expedition kit and equipment.
They have also encountered difficult terrain on their Antarctic adventure, with features known as sastrugi - sharp irregular grooves formed on the snow surface by wind erosion - proving hard to ski across.
Ed Parker, Team Noom Coach mentor, said: "Ivan Castro, the blind member of Team Noom Coach US, found this especially tough and took it with his typical stoicism."
The challenge is expected to take 15 days, after Ed Parker, Walking With The Wounded Co-founder and member of Team Noom Coach, shortened the race distance by about 37 miles.