I gave the original horse another single dose. I have not seen any more in about 4 days, from either horse. I've been washing his behind every day for weeks, as per instructed. This is gross, but might be helpful to someone: as I wash his behind, I sometimes use the sprayer nozzle. The stimulation of the spray sometimes made a worm come out; she must be right at the anal opening, ready to come out and lay eggs at night. It looked exactly like the online pictures I saw. I ground her into the dirt. No wonder the poor horse was itching like mad. Asked the vet yesterday about the small rice-like pieces in the manure. He said if they are round, they are immature pinworms. If flat, they are tapes. They were round, thank goodness. Hopefully we are getting in the clear with this.
I also asked him if the worms could live outside the horse and he said no. The eggs, however, are not too bothered by cold but will die in heat or dryness.
Good luck to anyone dealing with these little monsters--the pinworms, not the horses.