Giving her grandmother's address in Stoke-on-Trent, the horse was later left in her back garden.
The animal welfare charity said the horse, named Mr Melvin Andrews, was underweight and covered in mites.
Charlotte Melvin, from the charity, said a man dumped the horse at the house on Ford Green Road with "no words of advice" on 27 April, "leaving a very shocked nan".
She said Mr Melvin Andrews "clearly was not treated well before being abandoned" and the previous owner has not been found.
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The RSPCA has appealed for any information about Mr Melvin Andrews's previous home.

