A cough could be the result of any number of issues -- many of which can be cured without surgical intervention. However, from your description of a "goose honk" cough, I'm concerned that you could be dealing with tracheal collapse. This is a condition that is fairly common in small breed dogs, including Chihuahuas. And a "goose honk" cough is the most common symptom.
I would recommend you take your dog in for an examination by your veterinarian. If your dog is suffering from tracheal collapse, she would likely benefit from surgery -- either trachael ring or, depending on the severity, tracheal stent.
In any case, the place to start is definitely with a checkup to diagnose your pet's problem. Good luck, and let us know what you find out.
She had the problem for several weeks and then it stopped. I really think the cold weather was responsible! Thanks for your help!!!