I agree, it all depends on what triggers your child.
For my child (now nine, with chronic allergic asthma, diagnosed at 3 months with RAD and lung disease triggered by reflux, aspiration, and viruses) poor air quality in the summer is somewhat of a trigger, indoor allergens such as mold are a moderate trigger, and outdoor allergens such as grass pollen, ragweed and leaf mold are a huge trigger.
But cold -- not a problem at all. In fact, outside after the first hard frost of the season (which came early this year YAY!!!) is the time when he feels the best, needs the least medication (none really, we discontinue all meds in the winter and he does all his growing then), and generally feels great. He plays ice hockey and snowboards for hours on end with no problems.
For my son there are also things that are "sudden triggers" where he's exposed to them and immediately starts coughing and having a hard time -- cigarette smoke is the most obvious of these. But most triggers show up gradually a few hours later, or that night when he's coughing so loud it sounds like a gunshot in his sleep. The one time we did have a "cold" related attack it was about 10 degrees farenheit and he was just getting over pneumonia (still on antibiotics). That attack was very sudden. Since then we've been in much colder weather (e.g. ski vacation in Maine last year) and he hasn't shown any signs of trouble.
So, I wouldn't assume that cold is a problem. But I'd watch carefully and see. If it seems like it might be I'd think about a "turtle" (like a tubular scarf) you can cover her mouth with to warm the air before it hits her lungs, that might help her.