If you have the cold virus you really should stay home from work or school because your cold can be contagious to other people.
Also when you do have a cold virus you won't be feeling good enough to perform any work anyway so your productivity will also suffer as a result of having the cold.
I tried going to work in the office before when I had a cold and I felt miserable and told my boss that I needed to go home because I could not function properly.
My boss said it was a good idea to go home and stay home from work until the cold virus cleared up and someone else would take over my duties at work until I got better.
So yes I would highly recommend you stay home from work or school if you have a cold and call in sick.