The conundrum that runners face when we start to catch a cold of some kind is knowing whether or not it's okay to keep running despite feeling ill. For non-runners, there is no conundrum: When you feel ill, you rest up and get healthy. We runners, though, have a tendency to feel like our training suffers if we don't run for a few days.
The truth of this sentiment is probably debatable. For one thing, it may be impossible to separate the impact of being ill from the impact of not training for a few days. Maybe we just feel sick, and that explains why we don't bounce back immediately after recovering. For another thing, a great deal of this phenomenon is obviously mental. Taking a week off means losing a full week of training, which in "running psychology" feels like you've "fallen a week behind" all those other runners out there.
Nonetheless, all experienced runners have conflicting past experience with running while ill. In some cases, running when you have a cold is a great way to give yourself bronchitis. We've all been gone on an ill-advised run, only to return feeling a few orders of magnitude worse than when we left. But in other cases, going for a run seems to get us "over the hump" of the cold and somehow makes us feel a lot better than we did before. The problem is that there is no apparent regularity to these results.
I won't say that there is a steadfast rule for all people or all situations. Many people swear by one strategy or another. What I will say is that the lack of consistency in the results of running while ill seems to indicate that there is more than a little psychology involved here, and that this probably influences things more than any virus.
In the end, it makes the most sense to rest up and recover. There is at least a scientific basis for this; it seems to make logical sense. I believe that the counter-claim, the idea that you can sometimes recover more quickly if you run when you're ill, is a bit of runners' mythology.
So if you're feeling a little under-the-weather and wondering if you should take the day off, I say, yes. Take the day off. It won't hurt your training as much as you think it will, and you won't have to worry about the "risk" of making your cold worse. Just stay home and rest up.