You've a good chance of catching sight of them on North Hill overlooking Minehead, as there is a free-roaming herd here. But please don’t try and touch or feed them. They’re true wild ponies.
If you do want to cuddle one, head to the Exmoor Pony Centre near Dulverton. Here you can have a full hands-on experience and take one on a ride, or just visit and find out more about the work they do rescuing this rare breed.