SQL Server: cold backup, shutting down services?
Never heard such rubbish.

FULL or BULK LOGGED mode means you require log backups. SIMPLE means you don't.
You always require full backups.

Copying the MDF and LDF files isn't a backup and can potentially lose** you data if you are in a transaction as you shut SQL Server down.

If the mdf files are missing it means they aren't there because of finger trouble or this "backup" method. You can't lose mdfs unless someone removes the files or removes a drive when SQL Server is shut down

** Edit:

By losing data I mean "open transactions won't be committed". Typically, client code won't handle a retry and, say, log the error but not the data to be written.

Any data in committed transactions, no matter how old or new, will be safe