Expedition leader Al Fastier said the trip was the same distance (2012km) as Scott Base to the South Pole.
"The importance is Piha was dear to Ed's family and Ed and Mt Cook is where they did all the training for the trans-Antarctic expedition," he said.
Mr Fastier said they were hoping to raise about a million dollars for the hut restoration.
"Which sounds like a lot but when you consider Auckland house prices it's not much.
"At the moment we're just slightly over halfway."
Mr Fastier and Brian Blythe are driving Ferguson TE20s, the same Sir Ed and his party used to reach the South Pole and are being supported by a more modern Massey Ferguson MF5600.
The old tractors won't be breaking any land speed records.
"Someone passed me on a bicycle the other day," Mr Fastier said.
"They travel about the same speed as a push bike, they travel about 20km/h.
"I do a lot of cycle touring and that's about the same speed I travel at."
But the tractors are holding up so far.
"We've had a lot of teething problems along the way, just small things like loose wires and nuts and bolts," Mr Fastier said.
"But Brian's sort of a bit of an enthusiast on tractors, a bit of a mechanic, so he's probably the most important person on the expedition.
"It's a lot of good fun."
The expedition is expected to be completed on September 19.
People can donate to Expedition South via Givealittle at givealittle.co.nz/cause/expeditionsouth