Its a bit more complicated than that. If we had said "flu" then yes, for sure. But a cold isnt caused by a specific class of viruses or even one.It is a set of symptoms.
A cold is essentially infalamation of the mucosa membranes that is **not** caused by a specific virus or class of viruses. It is a set of symptoms that many different viruses all cause.
So its a bit more nuanced than that because literally what we call the common cold comes from damn near anything, including coronaviruses.