My asthma is well controlled, and I've been doing 3+ hour mountain bike rides 52 weeks a year for 7 years. I really love the winter mornings.
I was diagnosed at age 4 so I've got the triggers pretty well sussed, and cold air is one of them. I don't take Salbutamol/Ventolin with me because the nervous system side effects get me too much.
My techniques are:
Slow the pace, don't attack hills hard - which of course would mean a lot of big cold breaths;
Breathe in through my nose and out the mouth as much as possible - not very practical, but it helps;
If things start to tighten put my gloved hand over my nose and mouth, warm it with my breath, and breathe through it for a couple of minutes. Same effect as a scarf.
Now all I need is to get these damn knees back in line and I can start doing it again :-(