Persistent cold and cough

[Nanno]

I've had a problem with my goats coming down with colds this summer. It started with Finn, but he got over it within a few days. Next, Snickers got it and he can't seem to shake it. He gave it to Sputnik, who doesn't have it as bad but also doesn't seem to be getting better. Petunia started a runny nose the first day of State Fair (just over a week ago) and gave it to Nubbin before I brought them home. Nubbin's cold is very minor and she seems to be mostly over it. I thought Petunia was getting better but this morning her nose was crustier than ever. And I'm a little worried about Snickers. He's had this thing for a month now, and he gave it back to Finn about three days ago. He has a good appetite and plenty of energy and is growing like a weed, so I'm not worried that he's going downhill or anything, but I'm really tired of hearing him cough and seeing him come in with snot all over his face, not to mention I'm tired of being used as a walking handkerchief for a herd of snotty goats. How do we get rid of this thing??

The symptoms are mostly just snotty nose, no temperature. The snot is clear or white, usually not thick (although that seems to vary from day to day). They have a minor semi-wet cough. I was giving a multivitamin immune booster paste for a while, but it didn't seem to help. I recently started giving vitamin C drops to everyone. I'm not sure if they're helping or not. Is this something that just needs to run its course, or is there more I can do? I know there is no known cure for the common cold (and I'm pretty sure that's all this is), so I'm kind of at a loss what to do.