We bought a Morgan filly in 1988 and she arrived with warts, which then spread to some of our other young horses, since none of our herd then had been exposed to warts up until then. By early 1989 they'd run their course and we didn't have any more warts, not even on any of the young horses we raised or acquired after that spring. Then last summer we got a new horse that arrived with warts. That was in June--I'm not sure how long he'd had the warts, but I know he didn't have them in his spring photos, so he didn't have them very long. In less than a month they were gone. No one else caught them until last fall--then two of the young ponies had them on their noses. Those soon went away and now I just recently noticed that one other horse had some on his nose. This strain seems to be a short lived one so I'm not concerned--they'll soon run their course & be gone from the farm again.
Depending when your first show is there's a very good chance that these warts will be gone by the time the show rolls around, even if you don't do anything to try and get rid of them. That's the nice things about warts--leave them alone & they'll always go away.