It perpetuates a common myth.
[Click for larger, more readable version.]
There is no direct connection to getting a cold from having cold feet. It turns out that the rhinovirus (the cold virus) does do better in cooler temperatures, so that if the inside of your nose is cooler the virus can take off. And if you have cold, wet feet that can possibly chill you and thereby chill the inside of your nose. Except that if you have cold, wet feet you are probably in conditions where all the rest of you, including your face, is also cold and wet.
But if you have cold, wet feet and the rest of you, including your nose, is warm and toasty, you are not more susceptible. You can read more in my blog entry, The Germs Have Eyes, which includes references.