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Huber, who died earlier this month in Geraldine, was one of the world's last surviving members of the Nazi army unit the Waffen-SS.
Because of his work with Mt Hutt, he has a hut loft and a ski run named after him in the area.
Now, thousands are calling on Mt Hutt management to rename those.
Huber, who moved to New Zealand in the 1950s, joined Hitler Youth when Nazi Germany annexed his home country, Austria.
At 17, he volunteered for the Waffen-SS, serving both as a machine-gunner and then as a gunner in Panzer tanks.
His unit took part in the invasion of the Soviet Union, which claimed the lives of millions.
Huber received an Iron Cross first class for his service in the Battle of Kursk, by which time he had the officer's rank of Hauptsturmfuhrer, equivalent to a captain.
Earlier, he had received an Iron Cross second class.
In an interview with TVNZ, Huber said he had no knowledge of the war crimes committed by the Nazi forces, nor of the Holocaust, the Nazis' mass murder of about six million European Jews and millions of others.
"We, as soldiers never, never had the slightest inkling — maybe the high command," he said at the time.
"It never occurred to us what happened in Germany or Poland."
Because of his service in the Waffen SS, he was arrested and served 16 months in a military prison.
He was a former mountain guide in Austria and eventually moved to New Zealand in the 1950s and married, settling in Geraldine.
Huber has been referred to as the "founding father of Mt Hutt" and has a hut loft and a ski run named after him.
Mt Hutt Ski Area manager James McKenzie recently told Stuff that Mt Hutt is "happy to respect his legacy" after Huber "made a new start here and tried to put the past behind him".
The online petition claims Huber's role in the Waffen-SS is "not a legacy to be proud of and is an insult to all those murdered by the Nazis or who died fighting the Nazis".
"How lucky Mr Huber was to be able to make a 'new start', something that was not afforded to the victims murdered by the SS," Rob Berg wrote in the petition.
"We demand that Mt Hutt Ski Area removes the plaque honouring an unrepentant Nazi, who in a 2017 NZ TV interview said, 'I give it to Hitler, he was very clever' and admitted he volunteered to serve in the SS," Berg adds.
"We also demand Mt Hutt Sky Area rename the ski slope named after SS Officer Huber."
The petition has 2232 signatures.
Contacted by the Herald, Mt Hutt Ski Area Manager James McKenzie said he understands the views of those who signed the petition, however added that Mt Hutt does not plan to remove Huber's name.
"We understand the views of people who have signed the petition. However we cannot change the fact Willi Huber was integral to the inception of Mt Hutt," McKenzie said.
"We have acknowledged him on mountain because his involvement in the founding of our ski area was significant and we recognise him as an important figure in our history."