I remember back to when I was learning to drive, way back when it wasn't unusual to see a crank sticking out of a bumper, my dad told me to "NEVER set the emergency brake (parking brake today) in the winter!"
I'm chuckling about your experience with a wheel chock on a slick surface; been there, done that. Glad you got the brake mashed in time or I wouldn't be laughing.
PS I never trust a parking brake, mostly because some types only set one shoe and the vehicle can still role backwards. With my M923 I always chock the wheels when I park it.