As someone who has asthma and had it confirmed now, when I'm 42 years old, that my asthma is, in fact, triggered by the cold (cold weather, cold air, changes in the weather, eating or drinking something cold), I can sure sympathize with your daughter. I've had asthma since a child, usually triggered by talking or laughing too much, exercise, and the cold. The cold is the one that kept getting worse after I had my daughter, to the point that in the winter time, I would cough until I (literally) peed myself. It's not funny. I would cough so hard, it felt like my lungs were coming out of my chest, or that I would hack something up. Almost three years after having my daughter (who's now 10) I went on the lowest dose of Advair. That helped my asthma, especially in winter.
BUT, as I've learned these last two years, there are other reasons why a person gets asthma. I still have trouble with my asthma in the winter/cold, but if my body has enough Quercetin, then my asthma is drastically reduced. I also discovered that I have casein allergy, meaning I'm allergic to all cow products. Since I quit eating dairy and use goat, sheep, or coconut instead, I have noticed my asthma attacks have seriously diminished!! As well as my problems with pflegm and nasal and lung congestion. In fact, my asthma specialist can hardly believe that my asthma has improved as much as it has; he's in shock. I also have a severe intolerance to soy and gluten, along with some other foods, so maybe making sure I don't eat ANY of the foods my body is unable to tolerate is helping my asthma. I'm not sure, but I'm down to one puff a day on my Advair--and I live in WI, where it's cold more than it's hot!--and I might be able to go off Advair completely during the summer. YES!
I sincerely think asthma is related to something in the body that is out of whack, and as soon as you find out what the problem is and fix it, nine out of ten times, the asthma will go away as well. And if you can find the problem while young, your body has less time to get sick/really out of whack.
I'd recommend taking your daughter to a Naturopathic Doctor and having her tested for heavy metals (some of them can cause asthmalike symptoms), food allergies and intolerances, and for any malabsorption/nutrient depletion problems.
Good luck.