In most of my cars I use the throttle to throw it around when needed, BUT I have certainly used the hand brake in the snow... mainly because I'm a d!c&around when driving in the snow.
Shop truck blew a brake line in Chicago once and Mike pushed it all the way home on the parking brake, so I have seen it done. With either a dual circuit master or tandem masters, you should be able to stop if you lost a brake in any of our cars and most of our clients would then pull over and call AAA.