If I plug a hibernated hard-drive to another laptop, what will happen to the hibernated hard-drive?
No damage would occur; the hibernated drive would be perfectly readable, and safe to use for however long you like.
Deleting the hibernation state file (\hiberfil.sys on a Windows drive) would make it impossible to restore from hibernation if you ever put the drive back in its original laptop; you'd have to boot up like any other time you start up the machine from power off. That's the worst you can do to it, though.