You won't catch a cold, but there are very similar allergy symptoms.
An abrupt drop in temperature will cause constriction of blood vessels in the nose; this is know to cause an allergic reaction in some people, and this manifests itself very much like a cold (laryngitis, pharyngitis, etc...).
I thought it was allergies when I had it, but I had beige-coloured/green, thick mucous when I coughed, chills, sore throat, headache, fatigue, loss of appetite, runny nose, etc., so it feels like a cold in terms of symptoms too. When I get allergies, I never get sore throat and headache, and certainly not fatigue or chills.