It's a little different for automatics. With automatics, you'll have to contend with transmissionmission heat and clutch pack wear. This can be minimized with rev matched downshifts. Some modern automatics designed to be "sporty" can and will do that, while there's still plenty of brain dead electronically controlled automatics out there that don't, and slowly wait for RPMs to drop to a certain threshold before slipping into the lower gear. On older toyotas that are pretty slow and dumb at that, if I'm going down hill at any significant speed, I always just blip the throttle like I do with a manual to bump up the RPMs quickly and closer to what the engine speed will be to get it to downshift quickly. Not only that, it's my belief that wear is minimized this way.
but with manuals, you still have to worry about clutch wear if you don't rev match... most people don't know how to do this and just slip the clutch for downshifting... the motor lurches when that happens too and that also wears out the motor/transmission mounts