My Icelandic Pony, 5 years old, has a persistent cough.

History: Last fall, he was on a slaughter truck bound for Canada. The truck was turned back at the border because there was a sick horse (not my horse) on the truck. He was adopted from the kill pen, and about a month later, I brought him home. The rescuer said he'd had the cough since she brought him to her place. He coughed maybe six or seven times while we were there, which was about an hour. He came home in late December, and I had my vet out. He was given a course of antibiotics, and seemed to clear up almost entirely. Within a week after stopping the antibiotics, he was coughing again.

The vet said his lungs were clear.
No fever.
No nasal discharge.
Seems perky.
Cough severity vascillates, and I cannot discern any particular cause pattern. Sometimes he sounds like a child with a bad cold, very goopy sounding. Sometimes it's a very dry cough. Sometimes it's frequent, sometimes infrequent.
The horse has a very well-ventilated run-in stall and a very large dry lot (20 300 feet, roughly). We're in the Pacific Northwest, so there's been plenty of wet weather.

What are the most likely problems I could be facing here? If I have a vet out, what tests would be helpful? Is there anything I can do to help him myself?

I'm not opposed to having a vet out again, but it's expensive, and I'd like to have some questions to ask the vet to be able to tell whether they're a skilled diagnostician before making that investment again.

Optional Information:
Type of Animal: Horse
Gender: Male
Age: 5
Name of Animal: Lukka

Already Tried:
Vet visit. Antibiotics.