Iv the same problem with my jumping mare, she's perfectly healthy but when I start to excerise her she'll cough 3/4 times and then nothing. Iv jumped of a good few times and throughly checked her mouth and nostrils for any snot, mucus etc.. all clear.
I took her to the vet and ..well am not clued up on all the vetinary terms but in lay-mans terms he basically said she just clearing her throat, he gave me a white powder stuff to put in her feed for a few weeks, to be honest it was the biggest waste of £50, 2years on she'll still blurt out a cough and then she's gran.
Iv took her to another vet since and he sounded her and took a few blood tests... all clear. Literally just one of those things.. with her anyway.. I do think it would be a good idea to get her sounded by the vet just to check, just incase theres any underlying problems..