One month since the controversial Lapland New Forest theme park closed, Dorset Trading Standards said 5,000 customers have sought advice.
The Christmas attraction at Matchams on the Hampshire-Dorset border shut last month after thousands of complaints.
Some customers, who paid up to £30 a ticket, have been able to get refunds through their credit card companies.
But Trading Standards said people who have sought a refund from Lapland New Forest Ltd have had letters returned.
Lucy Penneck, from Bournemouth, has been trying to get a refund since her trip to the Lapland attraction on the opening weekend with her daughter.
Her father, a solicitor, wrote to the company's Brighton address, but his letter was returned unopened.
"It's not very good," said Ms Penneck.
"I feel we did not get an enjoyable day, I really want to pursue it to make everything right."
Her father Alan Turle, of Richards and Morgan Solicitors, added: "They [Lapland New Forest] have not been very quick to put things right for people."
The firm running the park said it had closed the attraction because of "intentional organised crowd manipulation and event sabotage".
Organisers had directed people to its website for information about obtaining a refund but the website has since closed.
No one from Lapland New Forest Ltd was available for comment on Monday.