It's a spirometry test. You breath into a tube attached to a machine. It measure how well your lungs perform. It also gives more information to the doctor. The other test for asthma that uses spirometry is a bronchial challenge test, which uses methacholine to induce a mild asthma attack. A positive along with patient history indicates asthma.
What is a Pulmonary function test? I have had athsma myself for 27 years, you would think I would know this. That could be the case then, my daughter did have the skin test right after all of this started 3 years ago. Maybe we should have it done again..
I would get her allergy tested again. It does sound like there is an asthma component there, considering she has a cough only in the winter time. Not everyone reacts the same way to allergy testing (skin *****). From my experience, I didn't even have a bump for the control (histamine), which everyone is supposed to have. I ended up seeing a second allergist and he explained it nicely. The first time I had my allergies tested for, I didn't show anything as my allergies were too "new" as he put it. I had them repeated a few years later and I showed more of a reaction, despite still having no bump for the control, my arm itched like crazy. I have dust mite, cat, molds, feathers etc.
I would certainly persist, till a diagnosis is given. I even had my asthma diagnosis taken away because of misinterpretation of tests, such as pulmonary function test and allergy testing. Your duaghter is also old enough to do the pulmonary function test. Some people just present more atypical then others, but a good doctor can work through that, and give the right treatment.