Basically, you quarantine sick horses and monitor them for changes that would require veterinary treatment---high fever, lethargy, going off feed, thick nasal discharge, labored respiration, etc. And provide good nutrition because that is where the body gets is energy and building blocks for building defenses against disease.
We don't have any good way to treat viral infections, they end up running their course or being fought off by the body. And without blood work or collecting nasal swabs it's impossible to say exactly what it is, but we just shouldn't treat these colds so nonchalantly. By doing so we put every horse our horses come into contact with at risk of getting sick--and not every horse will end up with a mild infection so we may lead to someone having a huge vet bill or even loosing their horse.
It doesn't surprise me that the vet didn't say much about it, because for years these little "colds"/upper respiratory infections haven't been taken very seriously by vets/breeders/trainers/owners. They've seemed like more of a nuisance than a real problem because your horse just coughed and was a little off for a few weeks, but we are really coming to understand how serious these viruses can be. A mutation of EHV has caused lots and lots of trouble for veterinary facilities, racing stables, show barns, etc in the last few years because the mutation causes serious and highly contageous neurological disease. And Influenza, one of the other common causes of respiratory infections in horses destroys the cilia---little hairs that line the resp. Tract and serve as a physical barrier to invading infectious organisms, irritants, debris--and it takes weeks for these cilia to regrow leaving your horse's body at a decreased ability to defend itself from airborn infectious organisms.
Here are a couple of articles for you to check out: http://www.thehorse.com/pdf/Vaccinat...ations_pt5.pdf http://www.thehorse.com/pdf/Vaccinat...ations_pt6.pdf