The sold-out, 90-minute North Pole Express experience is popular with families who take the train from East Tanfield station in North Yorkshire to see Santa and receive a Christmas present.
A volunteer from Tanfield Railway, where trains run on a rail dating to 1725, said the damage is “really disappointing”.
“There’s a lot of hard work put in (and) a lot of volunteer time put in,” David Watchman told the PA news agency.
“We’ve seen some extreme weather, we’re always prepared… but the winds were on a different level last night, and there’s only so much you can tie down and prepare for.
“It’s been totally different to what we’ve experienced before.”
The 32-year-old described the volunteer-run attraction, which was supposed to open on Saturday, as “a really magical show”.
“We’ve got some festive animals which the kids can meet and get their photograph taken with, we’ve got arts and crafts,” he said.
“And then you get on our steam train and (go on) a magical journey to the North Pole where you visit Santa at his specially built Grotto.”
The team at Tanfield Railway said they were “devastated” by the destruction of the North Pole at Andrew’s House station.
“We’ll do everything within our power to ensure that disappointment is only temporary,” they said in a Facebook post, which has had more than 250 comments of support from local people.
Mr Watchman added it was not until Saturday morning that volunteers “realised the extent” of the damage.
“We’ve got to admit we were keeping an eye on the weather. We didn’t expect it at the levels that we had here,” he said.
“You know, when we’ve got tents blown away and things like that, we realised (it is) a different level of weather storm.
“Seeing people visiting the railway, the smiles on people’s faces and the kids seeing Santa, (cancelling is) the last thing that we want to do.”
Mr Watchman said volunteers have been contacting ticket-holders and are hoping the North Pole Express will be ready to open by Sunday.
“As we speak, we’ve got a team of volunteers on the go, putting another tent up, fixing the buildings (and) clearing the trees,” he said.
“We’ve spent the last six weeks setting up for (this)… so we’re still hard at work trying to get things prepared for tomorrow.”