Authorities have at times been forced to close roads over the New Year across Llanelli because of the threat posed to motorists from the animals.
Llanelli's coast road was closed for most of the weekend because of the horses, which have also been blamed for damage to parks, a golf course and football fields.
A three-kilometre coastal stretch has been closed four times since the Christmas holiday period began because of the horses.
Most of the damage to reserves has been in Carmarthenshire Council.
A meeting in Llanelli on Thursday has been called to discuss the problem horses, which authorities suspect have been abandoned.
One golf course was described as unplayable as a result of horse damage, and the animals have been blamed for destroying fences along a 20-kilometre portion of the Millennium Coastal Park.
Local authorities have blamed irresponsible horse owners for abandoning the animals in the area to fend for themselves over the winter.
It is understood the animals are not microchipped but agencies are warning that where identification can be proved, prosecutions will follow.