Just thought you might be interested in this article related to this story. Interesting and from a “Science” site - though I doubt 100% uncontested.
title…"“Feed a cold, starve a fever” may be right"
It’s a bit like the evidence we have now that “leaching” or bloodletting may have had merit.
here is the original post
http://www.straightdope.com/classics/a5_154b.html
Funny: when I was a kid in England it was “feed a fever, starve a cold”.
Wisdom of the ancients and all that. 
Yeah, Cecil’s orig reply says that in 1574 it was “Fasting is a great remedie of feuer”…and possibly where it originated.
The idea behind starving a fever being the avoidance of giving your body anything to do that would raise its temperature, like digesting stuff or converting sugars to fat.
I’m not sure of the supposed wisdom behind feeding a cold though, other than the idea that you need to “keep your strength up” to fight off the infection. Personally, I’m never that hungry when in the grips of a nasty cold.