A flight attendant was then said to chip in with: "And we've got lots of wine and cheese."
Burns described the flying conditions as "hideous" but commended the Air New Zealand staff.
This week's wintry conditions had people sharing online their hair-raising flights into the windy city, notorious for its white knuckle landings.
Wind speeds were said to reach up to 109km/h at Wellington Airport on Thursday, prompting the cancellation of various regional services.
MetService predicted more rain for the capital over the weekend, and the wet weather is expected to continue well into next week.