I've had asthma for close to six decades. It seems now that the inhalable treatments are pretty effective, but they do have side effects. For me, the problems are that they mess with my voice so I either sound like a teenager, or else like Brando in The Godfather. Also, I get prone to oral yeast infections. A few decades ago, before steroids, cromoglycate powder inhalers did the trick with no side effects - but they had to be taken 4 times a day, so not as convenient. I don't know why this is no longer available - it was cheap and really worked for me.

Cold weather causes trouble for asthmatics primarily due to lack of moisture in the air. I can completely eliminate this by wrapping a loose-knit acrylic scarf across my nose and mouth. The scarf retains enough moisture from exhalation to moisturize the incoming cold air charge. You just have to find the right weight of scarf - nothing too thick or dense.
Hope you find something that works for you.