Antarctic City is a neutral megacity in the Antarctic, administering the Antarctic Territories. Mines and harsh 'back to nature' settlements like the Amundsen Outpost are out in the territories, as is the Ross Tek-Centre.The Atomic Wars have left a lush "Antarctic Jungle". 
Antarctic City's neutrality has made it a destination of choice for criminals: Nero Narcos had an untouchable account at the Bank of Antarctica and bent MC-1 Judges Jackson and Klee planned to flee there with stolen creds. It was introduced in the Shamballa world map and appears to be centred on the Australian Antarctic Territory.
In the 2116 Nepal Olympics, Antarctic City competed in taxidermy (competitor Sibling) and mountaineering. The entire mountaineering team were wiped out in a blizzard.
Judge Eckhart's ship crashed in the Territories, near the abandoned Ultima Thule Mining Complex. As this was neutral ground, various megacities could travel there to fight it out for Eckhart's knowledge. Antarctic City stayed out of it.
In late 2116, Mega-City One's Judge Wynter was sent to patrol the Amundsen Outpost as a disciplinary measure. Many of the outpost's children were dying as the environment prevented them developing an immune system and an influenza vaccine was flown out to them. Pirates under the command of Captain Smee attacked the vaccine's transport, trying to get chemical weapons on board; Wynter defeated them and secured the medicine. 
In 2117, a radio caller in Mega-City One referred to the "situation in Antarctica".
Antarctic City held the 2120 Olympics.
The Antarctic government handed three Total War members over to Mega-City One in 2126. Total War planned to retaliate by murdering the visiting Southern Cross sports team. Dredd prevented this - though the Judges had kept news of the plot from Antarctic City, so as to make sure the terrorists weren't aware they were being watched.
"Polar Judges" in green, fur-lined winter clothes and visors were shown in Mega-Special #1: "Constantly fighting against both hostile environment (Arctic Sector) and extremely hostile mining/prospecting community. Genetically modified to survive polar conditions." As no Arctic city was ever shown in the subsequent prog 701 world map, this is likely been retconned as Antarctic. One of these Judges was seen at the Hondo conference on Judgement Day.
Judges on outpost patrol have thick, heavy armour, oversized guns with harpoon/grapples, and heavily armed hoverbikes.
Mega-City One Judges have been sent to patrol Antarctican Territories as punishment. (Wynter's badge is an MC-1 design; possibly a mistake but 2000 AD's official tumbler stated it in 2013)
Antarctic City was one of the many cities infiltrated by the Martian Colonial Army. When these invaders were routed, heavily armed snow-dozers were at the forefront.