HardyWeinberg

I've had bad chronic asthma for decades, when living in cold places I never left the house in winter w/o a scarf. It's never been considered 'exercise induced' per se for me, just temp shock has always been a trigger.

You could try arranging a scarf around/in front of your neck/head (not wrapped tight around your face) so that the air you are breathing is warmed up/humidified by your in/ex-halations by the time you breathe it in. Create a warmer/humider microclimate around your nose/mouth.

The warming up pre-exercise doesn't ring any bells for me. Nor the proactive rescue-inhaler use. What I would do instead is wait for pulmonary tightness (which was always around the corner for me) and then use the albuterol reactively. 2 inhalations at a time, wait for improvement. (edit: that is specifically 'what I would do', not my recommendation for what I think you should do, you need to do some learning about how your body reacts to the combination of triggers, medicines, etc... you throw at it; I do think you should try the scarf/bandanna thing, though).

After finally giving up on ever hoping for any qualitative change in the asthma, I'm almost a week away from the last time I took any asthma medicine at all, I would never have thought that would happen.