The method that I use to remove gum from the bottom of my sneakers is to use a Suede/Nobuck Gum Eraser, which can be found in the Suede/Nubuck Kit they sell at Footlockers. They normally cost $5.99, so preferably you might want to buy one when they have Friends and Family sales, which should knock the price down by 25-30%. The reason why I prefer to use a S/N Gum Eraser is because it is a much faster method to remove gum in my opinion. The eraser will cause the gum to roll up and flake off whatever it is stuck to. I don't have to deal with ice water getting all over the place. Nor do I have to deal with the awful odors of Goo Gone or Goof Off.
We are planning to do a video tutorial in the near future. Just hang tight for the moment.