But Tim's father Richard, who founded the company back in 1970, suggested that if we came out right away it should be possible to sneak in a quick flight.
When we took off, the wind was already getting up and we could see the clouds moving in from the west. But as the Airvan zipped down the runway the golden tussock covering the landscape was still glowing bright sunshine, the shapes carved by ancient glaciers into the Mackenzie Basin stood out clearly and the waters of Lake Tekapo shone a glacial turquoise blue.
As we flew across the lake, heading for the rolling brown slopes of the Godley Peaks and Glenmore Station, Richard explained that because of the weather he wouldn't be able to follow the usual route, up the Godley River and down the valleys carved out by the Godley, Murchison, Tasman, Franz Josef and Fox Glaciers. Instead, we would head straight for the summit of Aoraki.
We didn't care. The foothills were impressive enough, though it was hard to imagine how this harsh landscape could possibly support flocks of 10,000 merino sheep on each station.
As we got close to the mountains we could see clearly that a thick layer of cloud was covering all the peaks and glaciers ... except for Aoraki whose massive bulk was actually splitting the storm and creating a clear path up to the summit.
Up that path we flew, with Tim climbing above the storm, until we were looking down on the 3497m summit, first climbed by three locals on Christmas Day, 1894.
We circled, looking down in amazement on the steepness of the slopes, wondering how anyone could possibly climb them. "Sometimes," said Tim, "We can see climbers. But not today."
Then, as the storm continued to advance, we retreated towards the safety of the airstrip. Tim warned things might be a bit bumpy and added, "To give you an idea of how strong the wind is, we were going 80kph getting here, going back we're doing 170."
When we landed Tim apologised again for not being able to offer the full experience. But I was delighted with the flight.
Indeed, in some ways, seeing Aoraki living up to its name by piercing the clouds, like some mighty warrior holding back an invading army, was even more impressive than the serene beauty of the flight I had watched earlier on a video.
CHECKLIST
Further information: See airsafaris.co.nz.
Jim Eagles flew as a guest of Air Safaris.