Does anyohe know whether it’s safe to operate the My Book Essential 3 TB drive in a horizontal position?

No problem as long as the drive is on a well ventilated area

I read in another posting (and verified this), the MyBook series is designed to operate in the vertical position to allow for convective cooling. While the disk will of course operate in the horizontal position, it will do so with warmer internal temperatures.

If the disk is well ventilated and you’ve got some air blowing over it then it would be ok to lay it on its side.