You might choose to simply reserve a server as a cold standby and not have it perform other functions, but this is rare. A cold standby will normally not contain any of the databases from the primary. It might not even have SQL Server installed. These servers are also normally powered off. If you are using a cold standby, I would suggest having it already preconfigured with the appropriate software in order to ease the fail over.
Cold standbys are usually much smaller than the primary production servers.
An example of a cold standbys is a Compaq 3000. These servers also do not carry the full storage capacity of the primary production servers. A cold standby is normally marked by two processes that must be performed during failover. The first one is to power on the server. The second one is to restore a full database backup.