<< Just wondering. I'm about to buy an old car with auto transmission. I live up on quite a steep hill and while I've driven an automatic for years, I've never bothered changing gears going up hills. >>
You only shift down when you're going downhill to activate engine braking. You might want to shift down out of overdrive if you have a dumb transmission and want to have better throttle response up a nasty hill. You'd usually have to floor the pedal or shift down out of overrdrive into a gear that gives better acceleration.
As everybody else said, it's not a good idea to let your car's weight roll into parking pawl. You don't have to go through a pain of putting in neutral, but apply your parking brake firmly and shift to park before releasing your foot brake.
I also discourage you from parking your car without using the parking brake up a hill. Parking pawl locks into a place rather than working by friction and it's fragile. If someone hits your car, it will break off the pawl and car goes rolling down the hill.