We live on a cow ranch here in the western U.S. and, of course have several cow ponies... no pets, just working stock horses. We keep them all on a strict worming schedule. There are several varieties of worms the horses can pick up by as simple an act as grazing.
What's best for your horse? Hard to say but a good veterinarian will be invaluable as a ally against these potentially deadly little critters. Frist thing a good vet will do is set up a progressive schedule for cleaning and eliminating them as much as possible. He'll also teach you how do do it with the various sources available today. Good investment...
Good luck! (What's your ponies name? Tells a lot about the owner, I think).