Hi Elissa,

My DD had this for a little while. The cough was residual to a cold she had had. It could be that Archie is just having difficulty shaking the cough from an illness. The colder air at night and in the morning can be enough to stimulate a cough - especially if he is breathing through his mouth. When we breath through our nose, the air is warmed up before it reaches the lungs. When we breath through our mouth, the air doens't get that same warming and so tempreture contrast can cause a cough.
Having said that, if the cough has been persistent for a few weeks, I would probably get it checked out just to be sure it hasn't (or won't) develop into something bigger.

HTH

MG