Cold plugging refers to the situation where a computer must be powered down in order to add or remove a component or to allow a device to synchronize data with the computer. Cold plugging is often used as an additional precaution to ensure a component is not damaged while being removed or replaced. It is especially used with modules that are volatile to static electricity such as circuit boards. A cold plug device that is hot swapped can cause malfunction and damage to the device or the system. Also known as cold swapping.
Techopedia explains Cold Plugging
In most PCs, the CPU and memory are examples cold pluggable components. That being said, CPUs are not always cold-pluggable -- they are often hot pluggable in high-end servers and mainframes. he opposite of cold plugging is hot plugging. A hot pluggable device can be replaced without shutting down the computer. A common hot swappable device that most people have used is anything using a universal serial bus (USB) connection. In certain contexts, a cold plug is defined as having the ability to remove or add a component without rebooting but it does not have the capability to identify the changes until rebooting. (In this case a hot plug would be defined as having the ability to identify changes without rebooting.)