A hot backup is taking a backup of the database while it is still up and running and it must be in archive log mode.
A cold backup is taking a backup of the database while it is shut down and does not require being in archive log mode.
The benefit of taking a hot backup is that the database is still available for use while the backup is occurring and you can recover the database to any ball in time. The advantage of taking a cold backup is that it is typically easier to administer the
backup and recovery process. Also, since you are taking cold backups the database does not require being in archive log mode, and thus, there will be a slight performance gain as the database is not cutting archive logs to disk