The shocked woman, unsure what to do with the pony, contacted World Horse Welfare who got in touch with the RSPCA.
The animal charity on Thursday released pictures of the pony stranded in the small yard of the house surrounded by wheelie-bins, garden furniture and a rabbit hutch.
RSPCA inspector Charlotte Melvin, who attended the property to check over the horse, said: 'You couldn't make this up.
'A 13-year-old girl responded to a plea on an online free ads site where a lady said she didn't want the pony anymore and that he would be put to sleep if no one had him.
'She gave her nan's address and the next thing that happened was a man just came along and dumped the pony there, no words of advice or anything like that - and leaving a very shocked nan.
'We don't know where this poor pony came from but he clearly was not treated well before being abandoned.
'We have come to a dead end in trying to find out further information so we are appealing for anybody who can help us to get in touch.'
The pony, who has been named Mr Melvin Andrews, is now in the care of World Horse Welfare.
Field officer Rachel Andrews, who transported the animal to private boarding, said she hoped the incident was not the start of a new trend.
She added: 'We're seeing sick or young ponies being dumped and abandoned when their owners no longer want them, and it would be a worry if online free ad sites are used in this way.
'Many provide advice on the commitment required to take on a horse.
'Every horse and pony deserves responsible ownership, which includes responsible breeding, selling and rehoming.
'We're just glad that Melvin the pony has settled in well at our Penny Farm Rescue and Rehoming Centre and has already shown himself to be lovely a little pony and we hope in time we can find him a good home.'
Anyone who has any information is asked to call the RSPCA's appeals line on 0300 123 8018 or World Horse Welfare at 08000 480 180.
Last month, the RSPCA revealed that the number of horses rescued by the charity has reached a four-year high, as the equine crisis continues to have devastating consequences.
The charity's annual Cruelty Statistics revealed that nearly 1,000 horses were rescued by the charity from cruelty, suffering and neglect last year (2017), and a staggering 928 horses are currently in the charity's care.