I do not usually get asthma at all, never have, but did get 'sickness induced asthma' from about 33 weeks on.
They gave me a script for an inhaler (a preventative) and I think I used it 3-4 times. It was never very severe though.

It did not affect my birth plan at all, nor did it affect my labour.
The midwives or doctors when I was in labour never even mentioned it or asked me how I was breathing lol As I said though, I am not usually asthmatic, and it was not severe.
HTH