I have very mild asthmatic symptoms.
They appear as a cough when running in cold weather (so I don't!) and a cough can appear after a cold or some other URTI.
I usually take ventolin when the cough appears or before I do exercise that involves jogging outside in coolish weather or skiing. This usually keeps it well under control.
Other things I do to keep the cough to a minimum is exercise regularly. Jog, cross train, cycle etc as well as simple weights. Also, eat sensibly and generally try to manage stress sensibly.
At the moment I am recovering from a cold and the cough's appeared too. I find I tend to cough more at night, esp when going to bed.Which is annoying. It feels like there's some tight bands around the lower half of my ribs and a funny pressure sensation at the top of my lungs. It feels like there's only about a 1/4 of the volume available. Also, it feels like I want to cough often but I try and resist that. This will last for a few more days (I hope) and then it should go back to normal. In the mean time I try and not aggravate the cough.
I am sorry I can't comment directly on your medication. Asthma's one of those tricky conditions that it can be very mild in one person and a potential killer in another. Manage it properly and sensibly and you should be fine. Ignore it at your risk.