These are usually rented from a vendor, but some of the larger corporations have built and maintain their own. They are usually well outside the geographic area so that they do not fall under the inherent risks of the primary operation. A cold site is a facility that has access to power and communications, and space for staff and equipment. The facility is basically a shell waiting for an equipped team to take over once the primary facility is lost. A cold site can be 10 to 20x cheaper than setting up and maintaining a hot site.
Some corporations mix both concepts.