Most runners get an occasional cold, and they wonder if they should run through the cold or take a day or two of rest. Each runner has to answer that question, because we all have different bodies and thus different energy-levels and different immune systems. Here are a few things to consider.
If a person has a strong immune system, the person probably won't get colds, because running, when done properly, should strengthen our immune systems. In fact, we can usually consider a cold as a sign from our body that we're doing something wrong, such as getting insufficient sleep, having too much stress in our lives, getting inadequate nutrition, or pushing ourselves too much in our training. I have a cold right now because I pushed myself too much in my two-hour run on Wednesday.
When we have a cold, we may take meds to help us breath, to suppress the symptoms of the cold so we can go into public activities and not cough and sneeze a lot, but those meds don't cure the cold. Only our body can cure the cold, and to do that our body must have enough energy to overcome the cold. Thus, getting rest, liquids, and proper nutrition when we have a cold will help our body have the energy it needs.
Should you run through a cold? My answer is "yes" if you feel pretty good and have a relatively high energy-level. My answer is "no" if you feel tired, down in the dumps, so to speak. When I was younger, I used to run through colds. Now that I'm older, I usually don't run in the "thin mucus" stage but will run in the "thick mucus" stage if I feel pretty good. I only get one or two colds per year, and they are usually from over training, so I don't have to worry much about running or resting during a cold. I know that over training is likely the culprit, and rest is the proper treatment for recovering from over training as well as from the cold.