"Starve a fever, but feed a cold." This saying plagues me every time I take the temperature of one of my girls. I always wonder where I learned it and if it is true. After researching it, I now know that this age-old maxim is not only not true, but that public-health officials have been working for years to debunk it.
The saying dates all the way back to 1574. At least the "starve a fever" part, for no one is sure when the second half was added. I guess maxims are more memorable when they contain pairs of things.
There seems to be no scientific evidence that supports fasting as a cure for a fever. However, when running a fever, it is best not to stress the body by not eating much. Chances are high (sorry for the pun) rich foods will have no real appeal if you're feverish. Stick to simple broths and toast.
If you have a cold there is nothing wrong with eating, but you just might not be able to taste it.