I'm planning to move the log files for the databases
msdb to a new drive.
But it seems that permissions aren´t copied with the directories and files; should I bother to move them over? (Or is that overkill?)
If you don't move the permissions too the service account under which SQL Server is running may not be able to access them.
You can use Robocopy to do this quite easily. I tend to use the following.
ROBOCOPY <source> <target> /MIR /SEC /SECFIX
More detaisl on this command can be found here
More Robocopy options can be found here