Ever been told this by an elderly person, and what are they trying to tell you?
Thanks,
Quasi
As far as I can tell by quick Googling, a cold in your neck is actually a cold, located in your neck. Go figure. 
Maybe it would help if you elaborated on the exact context in which elder people allegedly say this.
elderly, I mean of course.
“Sir, calm down, you’re going to give yourself skin failure. The symptoms you describe lead me to believe that you are suffering from bonus eruptus, a rare disorder in which the skeleton tries to jump out of the skin. The only way to stop it is through transdental electromicide. I’ll need a golf cart motor and a thousand volt capacimator, stat.”
-Dr Nick
I was treating one of my patients in the ER of the hospital where I work, and did that little thing people do when their neck sometimes goes stiff on them: rub, stretch, etc. The person who was with the patient commented that she thought I had “a cold” in my neck.
I have never before heard of this.
I am surprised you’ve never heard of this, Quasi, being a doc (or nurse, or whatever). In the olden days, various ailments were attributed to being exposed to drafts and such. One could have a cold just about anywhere. A stiff neck is a classic case. I believe the current-day usage derives from a “cold in the nose” which now we know originates not from being cold but from viruses. I am 45 and this usage is mostly from my grandparents’ era and before.
Just a whatever! 
Thanks
Q