The shop refuses a refund because I changed my mind

In most cases, yes. New Zealand law does not give consumers a general right to return goods just because they changed their mind, whether bought in a store or online. The Consumer Guarantees Act 1993 applies only where the goods are faulty, not of acceptable quality, not as described or not fit for a purpose you made known. A shop's return policy for change of mind is a voluntary concession, and it must be honoured as advertised, because failing to do so could mislead you under the Fair Trading Act 1986. Check the terms shown when you bought the coat, the website policy and any receipt. If the policy promised returns for unworn items within a certain period, the shop should follow it. If not, you may be limited to asking for goodwill or listing the coat for resale.