In this particular case it would have been handy to carry a large knife, pick or something like that in your pockets too. It's extremely hard to hoist yourself onto an ice slab, particularly in bulky gear, since you have nowhere to grab it. If you have something pointy that you can smash into the ice, it gives you something to hold.
I carry one of these. It comes with a window punch and seatbelt cutter, and the blade makes quite a good pry bar. The blade tip is blunt in favor of the screwdriver / pry bar role. The only thing the serrated edge did not cut so far has been stainless a/c control cable. I wouldn't want to be in any aircraft or vehicle without one in my pocket as I consider it a vital escape tool
Gerber Hinderer Rescue Knife 22-01534