A cold can severely complicate asthma for sure :(
IME it does not take long for your oxygen levels to get low and dangerously low to cause damage to the brain and other organs ... if he is not responding to the emergency puffer to relieve his symptoms he needs to go to the hospital and get a masking treatment and oxygen supplements!
If his asthma is chronic like that they have portable masking units for home and daycare ~ we use to have kids in centre in the winter months who had to get the machine verses the little 'puffer' for treatment!