If all you want to do is change the DNS servers, primary and/or secondary, there aren’t much impact. It will just restart the network and usually you’d loose one or two pings while this happens.
That’s a much bigger deal. Changing that in essence is a change of the name of the server. This is well documented in this document. IP Address and Hostname Changes
I would recommend you to change it on all nodes in the cluster. The impact is a little hard to say without knowing much more about your specific system setup. As always when you do changes that has a potential to impact user facing services it’s recommended to do this during a maintenance window so that the service is well aware of potential impact.
