Bodmin ponies could be abandoned and left to die because of the cost of equine passports, say some owners.
Grazing ponies are at risk because they are worth nothing to owners
New European rules which start on Monday mean owners must keep a record of drugs in horses.
They are aimed at preventing horses treated with certain drugs from being sold as horsemeat.
But Bodmin Moor commoners say it is bureaucracy which could cost an owner up to £100 for an animal which may be worth nothing.
Commoners have grazing rights on common land on the moor.
Steve Sandercock, chairman of the St Cleer and District Commoners Association, which has 76 members, said: "Some of the ponies on the moor are for grazing purposes only.
"The value of the horse is nothing at all, so they'll be abandoned. They won't bother to do anything with them."
The South West Equine Charity at Yelverton in Devon has had 20 calls from people in Devon and Cornwall in the last three weeks asking to take their animals. Normally they would only get one call a month.
Spokeswoman Maureen Rolls said: "I have a worry about Bodmin ponies because, unlike Dartmoor, they don't have an exemption that they only need passports when they come off the moor."
Dartmoor and the New Forest had met criteria for derogation, but that did not happen on Bodmin.
Defra minister Alun Michael said he understood the concerns but local people had been warned of the legislation.
He said: "We have enormous support from the horse industry and from vets because without it we would be in danger of losing the use of some medicines regarded as essential for protection of horses."
Cornwall County Council's trading standards department will be responsible for enforcing the legislation.
But animal health inspector John Pascoe said initially their role would be providing advice and guidance.
He said: "We are not going to be knocking on people's doors to see if they have passports.
"When we come across people transporting horses at shows or markets we will deal with the problems as and when they occur."