Can you go in for an operation if you have the common cold? If I have a cold will my surgery be postponed?

Maybe. It depeds on your overall health and the length or type of surgery that you may be having. If you are having fevers or a lot of coughing, then surgery may be postponed. If there are only symptoms such as irritated throat or nasal congestion, then surgery may be alright. If it is a longer surgery that is planned, you would not likely want to have a lot of coughing after surgery.
Yes. If you have no fever you should be able to have the operation - although for some types of surgery it will be cancelled.