Loads of us get colds, could it be caused by our ultra-chilly air conditioning?

It's unlikely to be the cold air but more likely the air-conditioning which is the problem.  In our hemetically sealed environments the chances of spreading air-borne diseases, such as colds and flu, are greatly increased. 

Air-conditioning systems vary considerably but the common element is that they must be regularly cleaned and maintained.  Ask about your employer's air-conditioning cleaning procedures and when it was last maintained.  It shoud be a minimum of once a year but the more often the better.  And is the system appropriate for the work being carried out? You may have more people now, or the nature of the work may have changed (more PCs etc) but it's still the same air-conditioning as twenty years ago.