Hey Cowtown Comuter,
I have asthma and live in a climate that gets pretty cold in the winter; around 15 degrees F when I leave in the morning for work. I have commuted by bike for over three years now, or three winters. I have had success using a scarf over my nose and mouth, but am definitely going to try a balaclava this year.
Also, when I have more difficulty with my asthma in the winter I have had to have my dose of Advair increased. Do you currently use any type of bronchiodilator? Advair is a combination of two drugs. The first drug is fluticasone propionate (Flovent) and the second drug is salmeterol (Serevent). Serevent is a long lasting albuterol, I believe.
Also, if you consider trying the balaclava or scarf idea, I would recommend not getting anything thicker than Polartec 200. I have found that trying to breathe through Polartec 300 is difficult when I'm exerting considerable effort, like climbing in the granny gear/small chainring. Whatever you end up using, you just want to make sure that you can easily breathe through it.
I hope I have helped.